1996 chevy s10 headlights will not burn on high or low beam .

1996 Chevrolet K1500 Suburban Daytime Running Light Module ...

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I would check the fuses first. Headlights are typically on a separate fuse then the parking lights. If the fuse is fine check and see if the Bulb is burnt out but it is rare for both lights to go out at the same time.

I probably should not be answering this as I'm no expert, but ...
Let's see now, DRL comes on when in gear and headlights off, emergency break off.
Silly question but, are headlights working manually (click on manually and verify both working)? High beams, low beams OK?
Check the fuse. The DRL fuse in the underhood fuse box and the label tells you which one. I think it's 31 or 32 but not sure.
Aftermarket lamps (esp the stupid blue lamps) can cause this if a higher wattage is used. (Burns the plastic lamp sockets).
Also check the DRL relay.

Check your head light bulbs, your truck has the dual filiment headlight bulbs one per side which does both high beam and low beam, 9007 bulbs.
If the low beam filiments are burned out only the high beam will work.
Also look into finding out if the headlight switch is gone bad.
The headlight module and or drl module maybe defective.

These trucks are known for bad multifuction switches.
the switch that i talk of is the signal switch , the handle is the switch, it bolts to side of steering column . this switch controls the signals and the headlights and high /low beams. the other thing is the headlight switch connector, the connector some times goes bad and starts to melt or just comes out of the connector. you will need to remove the cover to steering column, the screws are located under the bottom cover in holes. remove cover and check connector and then test for power if you have power going into switch but not coming out then switch is bad.

the last thing is to make sure the bulbs are good , make sure the headlight bulbs are good , and also the driving light bulbs, test for power at the connectors to those lights to.
You will need to do a little testing to find the problem.

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 .

[Information] For a 2002 Toyota Camry, the Daytime Running Lights (DRL) operate utilizing the High Beams (inner Lamps closer to the center of the vehicle front) at a reduced power.

[The troubleshooting process:] Review the Owner's Manual and ensure the test configuration matches the following criteria:
1. According to the 2002 Toyota Camry Owner's Manual (Check your Owners Manual):
"The DRL system will make your headlights come on at a reduced brightness when:
The light switch s in the "DRL" position.
The ignition is on with the engine running.
The headlight switch is off.
The parking brake is released."

2. Set the Test Conditions according to Step 1 above.

3. Check the headlight bulbs to ensure they are not burned out. If one burns out, there is a fair chance that the other would have burned out at the same time. Replace as necessary. In this case, if the high beams operate, the DRLs should also operate.
4. Test the system, ensuring the step 1 conditions are set. (Engine running, Multi-function Switch on Turn Signals in "DRL" position, headlight switch off (repeating what the manual says -- it should be obvious that in the "DRL" position, the headlight switch should be off / do not have the switch positioned to "High Beam"), and the Parking Brake "off").
5. If DRL lights do not work, check the engine compartment Fuse and Relay Box. there is a 5 Amp DRL fuse -- replace it with the spare. Test (step 4).
6. If it does not work, swap around or replace relays -- there are three (3). Any one of them could be bad (stuck or burned out). Test (step 4).
7. Other less likely possible issues could be that the Multi-function Switch is broken or a connection / wire is broken. [Beyond the scope of this process.]

My problem was that the test configuration did not have the engine running and parking brake off - Step 1. Problem solved with much thought, repetitive tests on the vehicle and going back to the basics -- what does the Owner's Manual say and where are the applicable fuses and relays located?

You need to start by checking the fuse for your headlights (low beams). The DRL could be be bad, but I have not seen them go out very often.

 I’m inclined to believe you have a headlight switch problem and here’s why. There are 2 fuses one for each of the headlights on the vehicle. For the daytime running lights (DRL) to operate the fuse and wiring to the right head light has to be good, because it supplies the power for both headlights in the DRL mode. The fuse and wiring for the left headlight has to be good because the DRL relay needs power from that fuse to operate. The DRL relay in turn provides a path through the left headlight and wiring to ground. When you pull back on the dimmer switch, you are activating the flash to pass circuit of the headlight switch assembly. Because the flash to pass mode works you then know that the high beam wiring and headlight bulbs are in good condition. This also tells you that the ground circuit for the headlight switch is good. In many newer vehicles, the headlight switch doesn't provide power to the lights. The headlight switch has now become the path to ground to complete the circuit. The headlight switch and the high/low beam dimmer control are one assembly so when you replace one you get the other free. Such a deal! My coffee bet is on the headlight switch assembly.

Ok look under the bagtterry tray, there is a black box bolted to the body, it is the headlight ground and has a really bad tendency to corode due to the design.