I don't remember if you can access the light bulb sockets with enough room to insert the end of a probe from a simple, inexpensive multitester (Lowes, Harbour Freight, Home Depot, etc have them)? It sure would make your life easier if you test for voltage to either the low or high beam light bulbs without having to remove the tupperware to remove the nose cone.
If I remember correctly, early year LTs had a problem with the brown ground wire to the headlight. It seems as if would easily loose electrical contact. Since it;s the ground for both low and high beams, both lights cease to function.
I seem to remember people finding another place to connect it from the head light onto the frame?
The plug on the wiring harness connects directly to the head light assembly on the left hand side, the clutch handle side. It uses a U shaped spring to hold the plug to the jack. You do NOT want to loose it!! If you do, you have to order a repair plug from BMW to get the retainer clip. I used hot glue to hold mine in place.
Here is a link to to what the plug looks like:
61_2484 - REPAIR CABLE MAIN CABLE HARNESS picture
part number 01*83 30 0 402 336*REPAIR PLUG, 3-PIN - NO. 6106110.04*1 *$15.81
The plug has 3 conductors, negative, plus to low beam, and plus to high beam. You can see the U shaped retainer clip in the pix.
You can check the plug by putting the minus probe into the socket and then checking plus socket with the plus probe. If I remember correctly the low beam stays on when the high beam is switched on. If so, turn the high beam on and check each plus socket.
If that checks out, you can verify a ground wire problem inserting the plus probe into the socket and then touching the negative probe to the frame. Make sure the negative contact point you try is bare metal. If the plug is getting 12 volts, when you connect the probe to ground you should get a reading of a little higher than 12 volts DC. It's important that you make sure the multitester is set to check DC and not AC or current.
One way to make sure you have a good ground point to check is the headlight socket is still grounded is to attach a wire to the negative battery terminal and run the wire into the headlight area so that you touch the negative ground probe to it while you have the plus probe inserted into the plus socket.
Since the negative post on your battery is still connected you don't have to worry if the test wire accidentally touches the frame.
Best from Tucson
PS: keep us posted on your progress with this