I got a bmw 1998 523i, and cannot turn the headlamp mai n beam off, without disconnecting the electric's to lamps

Could be any number of reasons why this happens . The headlamp switch , the dimmer switch the headlamp relay , the BCM - body control module , wiring , connections , ground etc..... Without testing no one on here could say for sure what's wrong . Do you know how to test electrical circuits ? Viewing wiring diagrams then using a DVOM - digital volt ohmmeter to test the headlamp electrical circuits . Possibly hooking up a scan tool an checking headlamp switch input data to the BCM an seeing if the BCM is energizing the headlamp relay .
Free wiring diagrams here http://www.bbbind.com/free-tsb/ Enter vehicle info. year , make , model an engine size. Under system click on lighting , then under subsystem click on headlamps . Click the search button then click on the blue links .

https://www.youtube.com/watch?v=SO-eKuhCOqc&t=125s

https://www.youtube.com/watch?v=YaYtCVBodpw&t=98s

Headlamps
You can use the headlamps two different ways.
• Place the headlamp switch in the HEAD position for normal operations.
• Place the headlamp Switch in the OFF position for automatic lamp control (ALC) operation. During ALC the low beam headlamps are on for daytime running lamp (DRL) operation in daylight conditions or low beam headlamps and exterior park lamps on in low light conditions.
The DRL/EXT Fuse in the top underhood junction block supplies battery positive voltage at all time to the coil side of DRL relay, left low and high beam headlamps. The EXT LTS Fuse in the top underhood junction block supplies battery positive voltage at all time to the right low and high beam headlamps.
For normal manual low beam operation when the headlamp switch is placed in the HEAD position, ground is applied from G203, through the low beam contacts in the headlamp switch to the body control module (BCM).
The BCM then applies a ground to the headlamp relay control circuit. This energizes the headlamp relay in the left I/P junction block allowing ground from G201 to be applied through the switched contacts of the headlamp relay, through low beam contacts in the headlamp dimmer switch then to the left and right low beam headlamps, illuminating them.
For high beam operation the headlamp dimmer switch is placed in the HIGH position, ground is then applied from G201 through the switched contacts of the headlamp relay, through high contacts of the headlamp dimmer switch to the left and right high beam headlamps, illuminating them.
When the dimmer switch is placed in the HIGH position, the indicator lamp input to the BCM is pulled low. The BCM then sends a class 2 message to the instrument cluster in order to illuminate the high beam indicator lamp.
If the headlamp switch is left in the HEAD position, the inadvertent power control feature will turn off the headlamps after 10 minutes after you turn the ignition switch to the OFF position. If you place the headlamp switch in the head position after the ignition switch has been turned OFF, or if the ignition switch is in ACCY position, the headlamps will remain on until you turn them off or until the battery runs dead.

Here is how they are suppose to work .
Headlamps
The headlamps may be turned on two different ways. First, when the driver places the headlamp switch in the HEADLAMP position, for normal operation. Second, with the headlamp switch placed in the OFF position, for automatic lamp control (ALC). During ALC, the headlamps will be in day time running lamp (DRL) operation in daylight conditions, or low beam operation in low light conditions. The LH HDLPand RH HDLP fuses, supply battery positive voltage from the underhood junction block to the left and right headlamps. The circuit continues through both low and high beam lamps, then back to the underhood junction block. The low beam and high beam circuits continue to the headlamp switch. The low beam and high beam circuits also provide the body control module (BCM) with both low and high beam inputs. The headlamp switch includes the dimmer switch and the flash-to-pass switch. When the headlamp switch is placed in the HEADLAMP position a path to ground is provided. Ground is provided at G201. Depending on the position of the high/low beam switch, either the low or high beam circuit will now have power and ground.
The LH HDLP fuse in the underhood junction block, supplies battery positive voltage to the automatic lamp control (ALC) headlamp relay coil circuit. The ALC relay switch circuit is connected to the low beam circuit at the headlamp switch. When the headlamp switch is placed in the OFF position, the BCM will automatically turn on the low beams in low light conditions. The BCM energizes the ALC relay, closing the switch contacts and grounding the low beam circuit. Ground is provided at G201. With the headlights in the low beam position, the high beams may be momentarily turned on or flashed with the dimmer switch handle. The flash-to-pass feature is accomplished by pulling the dimmer switch handle toward the driver. The headlights may be switched to high beam with the opposite movement of the dimmer switch lever. When the headlamp dimmer switch handle is pulled toward the driver, the flash-to-pass switch closes grounding the high beam circuit. Ground is provided at G201. Both high beams will remain on until the driver releases the switch handle.
If the driver places the headlight switch in the HEADLAMP position , the headlights will remain on until turned off or the battery runs dead.

Finding a wiring diagram to use along with a DMM - digital multi-meter (voltmeter ) To test the electrical circuits for the headlamps B+ power & ground side of the circuit is the way to find a fix .
Watching a few basic electrical testing video's on youtube may help you .
Basic Electricity for Service Techs Ohm law Current Flow Opens Shorts
How to Use Multimeter to Troubleshoot Common Problems
The Trainer 18 Electrical Testing Tips
Can take years to learn how to trouble shoot automotive electrical systems properly .

It's probably the switch , but testing to know for sure is alwasy a good idea .

Headlamps Inoperative - High Beams
Step
Action
Value(s)
Yes
No
1
Did you perform the Daytime Running Lamps (DRL) System Check?
--
YES - Go to Step 2
NO - Go to Daytime Running Lights (DRL) System Check
2
Disconnect the turn/hazard headlamp switch connector C1.
Connect a fused jumper between terminal B of the turn/hazard headlamp switch assembly harness connector C1 and ground.
Do the high beam headlamps operate?
--
YES - Go to Step 3
NO - Go to Step 4
3
Replace the turn/hazard headlamp switch assembly.
Did you complete the repair?
--
Go to Daytime Running Lights (DRL) System Check
--
4
Repair the open in CKT 1200 between the turn/hazard headlamp switch assembly. Refer to Wiring Repairs in Wiring Systems.
Did you complete the repair?

Daytime Running Lights (DRL) System Check
Step
Action
Normal Result(s)
Abnormal Result(s)*
1
Turn the headlamp switch to the HEAD position.
Turn the headlamp dimmer switch to the LOW position.
The low beam headlamps are ON.
The high beam headlamps are OFF.
Headlamps Inoperative - Low Beams
2
Turn the headlamp switch to the HIGH position.
The high beam headlamps are ON.
The high beam indicator is ON.
The low beam headlamps are OFF.
Headlamps Inoperative - High Beams
3
Turn the headlamp switch OFF.
Turn the ignition to ON.
Disengage the parking brake.
The high beam headlamps come ON at a reduced intensity in approximately 30 seconds.
Daytime Running Lamps (DRL) Inoperative, Headlamp Switch Operates Normally
* Refer to the appropriate symptom diagnostic table for the applicable abnormal result.

It is located in the under hood fuse/relay box . It's non -replaceable ,if bad whole fuse box has to be replaced ! The low beam headlamps may be turned ON in 3 different ways:
?€¢
When the headlamp switch in the HEAD position for normal operations

?€¢
When the headlamp switch is in the AUTO position, for automatic lamp control (ALC)

?€¢
When the headlamp switch is placed in the AUTO position, with the windshield wipers ON in daylight conditions, after a 6 second delay

Battery voltage is applied at all times to the coil and switch sides of the LOW BEAM PCB Relay located in the underhood fuse block. When the headlamp switch is placed in the HEAD position, ground from G202 is applied through headlamps ON switch signal circuit to the body control module (BCM), signaling the headlamps ON request. In response to this signal, the BCM applies ground through the headlamp low beam relay control circuit energizing the low beam relay. With the relay energized, battery voltage is applied through the switch side of the relay, the left and right low beam fuses, and the low beam supply voltage circuits illuminating the low beam headlamps. Ground for the left headlamp is provided at G101 and the right headlamp at G100.
Low Beam Relay Test

1. Ignition OFF, disconnect the C2 harness connector at the underhood fuse block.
2. Connect a test lamp between the control circuit terminal A5 and B+.
3. Ignition ON, command the Low Beams ON and OFF with a scan tool. The test lamp should turn ON and OFF when changing between the commanded states.
?‡'
If the test lamp is always ON, test the control circuit for a short to ground. If the circuit tests normal, replace the BCM.



?‡'
If the test lamp is always OFF, test the control circuit for a short to voltage or an open/high resistance. If the circuit tests normal, replace the BCM.


4. If all circuits test normal, replace the underhood fuse block.
5. Ignition OFF, disconnect the harness connector at the inoperative low beam headlamp. Test for less than 5.0 ohms between the ground circuit terminal B and ground.
   ?‡'
   If greater than the specified range, test the ground circuit for an open/high resistance.
   

   Connect a test lamp between the supply voltage circuit terminal A and ground. Ignition ON, command the Low Beams ON and OFF with a scan tool. The test lamp should turn ON and OFF when changing between the commanded states.
   ?‡'
   If the test lamp is always ON, test the supply voltage circuit for a short to voltage. If the circuit tests normal, replace the underhood fuse block.
   

   
   ?‡'
   If the test lamp is always OFF, test the supply voltage circuit for a short to ground or an open/high resistance. If the circuit tests normal, replace the underhood fuse block.
   

   If all circuits test normal, test or replace the low beam headlamp.
   

It's probably the lighting control module , but without doing some electrical testing that is just a guess !
Battery positive voltage (B+) is applied at all times to the lamp control module (LCM) through the underhood junction block HDLP MaxiFuse® and CKT 1242 (RED).
When you place the headlamp switch in the HEAD position, the headlamps input to the LCM is grounded. The LCM then applies battery positive voltage (B+) through the underhood junction block HDLOBML fuse and HDLOBMR fuse, which feed the left low beam headlamp and the right low beam headlamp respectively. When you activate the headlamp dimmer switch by pulling on the multifunction lever until the switch clicks, CKT 524 (PPL) is grounded to the LCM. The LCM then removes battery positive voltage (B+) from the low beam headlamps and supplies battery positive voltage (B+) through the underhood junction block HDHIBML fuse and HDHIBMR fuse, which feed the left high beam headlamp and the right high beam headlamp respectively.

Twilight Sentinel Circuit Description
Twilight sentinel determines whether the daytime running lamps (DRL), or the exterior lamps and the low beam headlamps at full intensity should be on based upon the signal of the ambient light sensor. When the ambient light sensor detects daytime, the twilight sentinel turns on the DRL. When the ambient light sensor detects darkness, the twilight sentinel turns on the exterior lamps and the low beam headlamps at full intensity. The twilight sentinel also keeps the lamps on for a delay period of 3 to 180 seconds under the following conditions:
• The vehicle is in PARK.
• The ambient light sensor detects darkness.
• The ignition switch is turned to the OFF position.
You may turn off the twilight sentinel manually. When it is dark and the gear selector is in PARK, pushing the twilight sentinel switch to OFF will turn off the headlamps and exterior lamps. Pushing the twilight sentinel switch to OFF again will turn on the headlamps and the exterior lamps. If the gear selector is not in PARK, pushing the twilight sentinel switch will have no effect.
The F- switch is just an input from the LCM - lamp control module .
Do you know how to test control module inputs an outputs ? Very easy to fry a module if you don't know how to do it .
Also have a full scan of all modules on the vehicle , could have DTC'S - diagnostic trouble codes stored . Not for the OBD 2 engine computer . The instrument cluster , BCM , LCM can all set codes too, related to lighting an someother thing's .
ECM Inputs and Outputs Diagnosis

Electric Testing Techniques You Need to Know

You can find free wiring diagrams here http://www.bbbind.com/free_tsb.html Enter vehicle info. year , make , model and engine ! Under system click on lighting ,then under subsystem click headlamps . Click the search button then the blue link . The first diagram you will see at the top the power supply to the LCM , down a little you will see the headlamp switch , ambient light sensor . Now if you want to start replacing thing's without testing good luck !

Headlamps
The headlamps are operated when the driver places the headlamp switch in the HEADLAMP position. The LT HDLP and RT HDLP fuse in the IP fuse block, supply battery positive voltage to both the left and right headlamps. The low beam and high beam circuits continue to the headlamp switch. Depending on the position of the dimmer switch, either the low or high beam circuit will now have a path to ground. Ground is provided at G204. The low beam and high beam circuits also provide the body control module (BCM) with both low and high beam inputs. The headlamp switch includes the dimmer and the flash-to-pass switch.
If the headlight switch is left in the HEADLAMP position, the headlights will remain on until turned off or the battery runs dead.
Daytime Running Lamps (DRL)
Any function that turns on the headlights will cancel the daytime running lamps operation. The LT HDLP fuse in the IP fuse block supplies battery positive voltage to the daytime running lamp (DRL) relay coil circuit. The DRL relay switch contacts are connected to the low beam circuit. When the headlamp switch is placed in the OFF position, the BCM will turn on the daytime running lamps. The BCM energizes the DRL relay, closing the switch contacts and grounding the low beam circuit at G204. The DRL illuminate the low beam headlights at a reduced intensity. The DRL will operate when the ignition switch is in the RUN position, the gear selector is not in the PARK position and the parking brake is released. When these conditions have been met the DRL will illuminate.
DRL operation in Manual Transmission equipped vehicles will occur when the ignition switch is in the RUN position, and the parking brake is released.

Probably the dimmer switch . But without testing that would be just a guess . Turnning the headlamps on Any function that turns on the headlights will cancel the daytime running lamps operation..
No ,don't think the DRL relay has anything to do with it .

View wiring diagrams an testing the electrical circuits at the dimmer switch would be the proper way to diagnose .

1. Open the hood.
2. Remove the park/turn signal lamp assembly.
3. Remove the headlamp retainer pins.
4. Pull out the headlamp assembly in order to access the electrical connector.
5. Disconnect the electrical connector.
6. Remove the bulb from the headlamp assembly by twisting the bulb counterclockwise.

INSTALLATION PROCEDURE

IMPORTANT:

• Replace a high beam bulb with another high beam bulb. The high beam bulb has a red gasket.
• Replace a low beam bulb with another low beam bulb. The low beam bulb has a gray tip and a yellow gasket at the base.

1. Install the new bulb to the headlamp assembly by twisting the bulb clockwise in order to lock in place.
2. Connect the electrical connector to the bulb.
3. Install the headlamp assembly.
4. Install the headlamp retainer pins.
5. Rotate and lock the pins in place.
6. Install the park/turn signal lamp assembly.
7. Inspect the operation.

The front bumper must be removed. After it is removed there are three Hex bolts securing the headlamp to the car. 2 visible (1) not so visible resides in a hole on the right of the drives lamp, left on the passanger lamp. Ensure you disconnect the battery PRIOR to starting this job. If you are replacing HIDs the ballast should be your first choice, then bulbs.
Here is the information on the bulb:
HID Lamp (Low Beam), Replacing
WARNING:HIGH VOLTAGE.Always disconnect negative (-) battery terminal prior to servicing any parts of the HID lamp system marked with the yellow "HIGH VOLTAGE"symbol.After disconnecting battery, briefly turn headlights on and off in order discharge any residual voltage.
CAUTION:
Before beginning repairs on the electrical system:
· Switch off all electrical consumers.
· Switch ignition off and remove ignition key.
· Disconnect negative (-) battery terminal.
· When disconnecting and reconnecting battery terminals, observe all applicable Notes and torque specifications, as well as instructions on performing OBD program and electrical system function .
Removing.Activate "jacking" mode.Disconnect battery.Remove appropriate front wheel.Remove front left wheel housing liner.
Loosen locking bolt -1- a few turns.
Release retainer tabs -arrows- and remove housing cover for low beam from headlight housing.Disconnect electrical connector -1- at ignitor.
Turn ignitor -2- counter-clockwise -arrow- and remove.Disengage spring clip -1-.
Remove HID lamp -2- from headlight housing.

1. Open and support the hood.
2. Remove the grille.
3. Pull up on the retaining tabs in order to remove the headlamp assembly from the headlamp panel.
4. Disconnect the headlamp leveling electrical connector from the motor/actuator if equipped.
5. Disconnect the headlamp electrical connector from the headlamp assembly.
6. Remove the side marker socket from the headlamp assembly.
7. Remove the park/turn socket from the headlamp assembly.
8. Remove the headlamp assembly from the headlamp panel.
9. Remove the access cover from the rear of the headlamp.
10. Disconnect the electrical connector from the socket.
11. Rotate the bulb and socket counter clockwise in order to remove the bulb and socket from the housing.
12. Disconnect the electrical connector from the socket.
13. Remove the bulb and socket from the headlamp.

Replace the low beam bulb with another low beam bulb. The low beam bulb has a gray tip and a grey socket.

your owner manual will list the bulb. It is expensive. tascafordparts.com for discount from Ford Dealer

here's 2003, don't have 2004

Navigator high intensity discharge (HID) headlamp

1. Remove the front radiator air deflector.

1. Remove the three bolts and the headlamp assembly.
• Disconnect the electrical connectors.

8. Remove the headlamp bulb protective cover(s).

• Remove the HID lamp cover.
• Remove the high beam cover.
• Disconnect the electrical connector and push the grommet into the headlamp assembly.

1. Release the spring tabs and remove the HID low beam bulb.