What can cause a headlamp to be out besides a bad bulb?

Question edited for clarity.

Fuses 4 and 8, but there is also a relay involved.

Fuse Box Diagram Mercury Mountaineer (1997-2001)

https://fuse-box.info > mercury > mercury-mountaineer...

Here you will find fuse box diagrams of Mercury Mountaineer 1997, 1998, 1999, 2000 and 2001, get information about the location of the fuse panels inside ...

Mercury Mountaineer (1997 - 2001) - fuse box diagram

https://www.autogenius.info > mercury-mountaineer-19...

Aug 11, 2018 - Mercury Mountaineer (1997 - 2001) - fuse box diagram. Year of production: 1997, 1998, 1999, 2000, 2001. Passenger compartment fuse panel.

Mountaineer » Fuse Diagram

https://knigaproavto.ru > Fuse Box Diagram > Mercury
Fuse Box Diagram Mercury Mountaineer; engine 4.0 L Cologne V6 and 5.0 L Windsor V8 (1996, 1997, 1998, 1999, 2000, 2001)

Principles of Operation
The smart junction box (SJB) monitors the headlamp switch position by sending multiple voltage reference signals to the headlamp switch. When the headlamp switch is in any given position, that input signal is routed to ground.
The SJB also monitors the multifunction switch for a flash-to-pass or high beam request. There are 2 voltage reference circuits which monitor this. When the multifunction switch is in the FLASH-TO-PASS or HIGH BEAM position, the voltage signal is routed to ground.
NOTE: The flash-to-pass feature does not require any input from the headlamp switch.
When the SJB receives an input requesting the headlamps on, the SJB supplies voltage to the low beam and high beam bulbs as necessary.

Inspection and Verification

1. Verify the customer concern.

1. Visually inspect the following for obvious signs of mechanical or electrical damage.
   
   Visual Inspection Chart Mechanical Electrical
   • Headlamp switch
   • Multifunction switch
   • Battery junction box (BJB) fuse(s):
     • 19 (40A) (low beams)
     • 20 (20A) (RH ballast)
     • 31 (20A) (LH ballast)
   • Smart junction box (SJB) fuse 1 (20A) (high beams)
   • Circuitry
   • Bulbs
   • High intensity discharge (HID) bulb (Montego)
   • Ballast
   • Headlamp assembly
   • SJB

1. If an obvious cause for an observed or reported concern is found, correct the cause (if possible) before proceeding to the next step.

NOTE: Make sure the headlamp switch is in the OFF position.
NOTE: Make sure the multifunction switch is in the LOW BEAM position.

1. If the cause is not visually evident, connect the diagnostic tool to the data link connector (DLC) and select the vehicle to be tested from the diagnostic tool menu. If the diagnostic tool does not communicate with the vehicle:
   • check that the program card is correctly installed.
   • check the connections to the vehicle.
   • check the ignition switch position.

1. If the diagnostic tool still does not communicate with the vehicle, refer to the diagnostic tool operating manual.

1. Carry out the diagnostic tool data link test. If the diagnostic tool responds with:
   • CAN circuit fault; all electronic control units no response/not equipped, refer to Section 418-00 .
   • No response/not equipped for SJB, refer to Section 419-10 .
   • System passed, retrieve and record the continuous diagnostic trouble codes (DTCs), erase the continuous DTCs and carry out the self-test diagnostics for the SJB.

1. If the DTCs retrieved are related to the concern, go to the Smart Junction Box (SJB) Diagnostic Trouble Code (DTC) Index.

1. If no DTCs related to the concern are retrieved, GO to Symptom Chart .

Replace fuse. If fuse blows again it could be the ballasts have gone bad .

check in this order: 1)fuse box underneath steering wheel, 2)check both headlamps be sure to test on high and low beam, 3)use current tester just before the switch to make sure there power, 4)test wire prior to switch then all way to bulbs checking for power. replace bad sections as needed or repair wire.

Well, with the choices you have presented I would have to choose bulbs. Fuses do not cause electrical problems, electrical problems cause blown fuses. So, that automatically eliminates the fuse as the possible cause of your problem.

On the other hand, your problem could be caused by anything from blown bulbs to a defective headlamp control switch to a malfunctioning multiplex control unit or a bad DRL module.

Personally, I would turn the light switch on and check for power and ground at the headlamp bulb connector. If there is power and ground, then the bulb is the cause of the problem. If there is no power and ground, then you must properly diagnose your headlamp circuits to locate the fault.

Both your low beam and your high beam is protected by the same fuse, so it makes sense that the fuse is OK if the high beam is working on the passenger side. There are 3 fuses for the headlamps. Fuse #13 in the Battery Junction Box (20 Amp). If this fuse is blown, the headlamp relay will not have any power and neither high nor low beam on either side will work (you will have no headlamps at all) Then there is Fuses #2 and #3 (15 Amp) in the Battery Junction Box. #2 goes to the left low and high beam and #3 goes to the right low and high beam.
The headlamp switch uses a SINGLE CIRCUIT to control BOTH sides at the same time, so if one side works, the switch cannot be the problem. The headlamp relay provides power for fuses #2 and #3 and we already ascertained that these fuses must have power since we have working lights on both sides, so the relay cannot be the problem. A replacement bulb has already been tried, so that pretty much leaves us with a bad lamp socket. (Most likely cause) or a bad connection at splice #S122, which is located in the main wiring harness near the breakout for the left headlamp. (RED/BLACK wire)

check fuses in box near coolant reservoir.fuses should be marked on box cover.hi/lo and left and right fused individually for atotal of four fuses for headlamps.

no fuse for that for the bulbs acts like a fuse does when worn out for they just blow out. They are insulated inside a glass bulb too protecting the system from causing any problems. If the headlamps do not operate replace the headlamp switch if the bulbs are any good which I assume they are

There should be a main fuse box under the hood. The headlights have a main fuse for each side. There should be one for the left and right headlamp. Check the fuse for the r/f headlamp. If it is blown, then that is the cause for the headlamp not to work. Replace with a new fuse and it should be good to go. If not, check the bulb itself.

main fuse box? are you referring to the one in the car or the one under the hood as the main fuse box? There are two