Is the car running or turned off?
If you look at the post that has the schematic drawing there are two fuses in the central junction box under the dash number 10 and number 4 which are both ten amp. At this point there are seperate circuits for each lamp so it would most likely be before that. I would put a test lamp on both side of both fuses and see if the test lamp flicker at the same time as the lights, if it does then we have to back up farther towards the battery.
The commonality between the two lamps before the fuses is the mutltifunction switch which you replaced. Then the Headlight switch then you go back to top of the page and it reads HOT AT ALL Times connection. This will come from the power junction fuse box next to the battery. If Mid Life Crisis #388 could post up the wiring diagram for central fuse box and alternator is would help me narrow this down.
In the old days the fuseable link was typically on the HOT side of the starter solenoid. Usually a BIG red or black wire and about two inched down the wire get a bit smaller with what appears to be black heat shrink, that is the link. Now on our car there is a big black wire with an orange strip that goes to the input of the central fuse box. This black wire with orange strip goes into a small white piece that has Fuseable link printed right on it then this turns into two beige wires that go into the power distribution fuse box next to the battery.
This sounds like there is severe corrison on a fuse, a burnt wire, a burnt fuseable link or a fuse that has the internal element that is broken. (When it is cold it relaxs and touches when it gets warm it moves and opens the circuit, same way the old turn signal flasher work.) After looking at my car, the fusable link is between the alternator and the central fuse box so it isn't likely this is the cause if the car is not running. This is because if the car is off the big red wire coming from the battery to the central fuse box is providing power. My owners manual on page 136shows that the fuse 2 30 Amp MAXI fuse (green) closest to the engine center row is the fuse for the low beam head lamps circuit. The drawing shown in the manual shows the latch and hinge for the central fuse box backwards. So i pulled fuse 2 closest to the engine in the middle row and my headlight quit working.
Pull this fuse out and look down at the mating connections. Look for corrision overheating or a defective fuse, or swap it with fuse ten which is for the parking lamp.
You can also put a test lamp on fuse two on the power distribution box next to the battery, one side at a time and see if it flickers on either side when the headlights flicker. This fuse is hot all the time but no current going thru until you turn on the headlight.
The last thing would be to disconnect the battery and turn the power distrubtion box over and look at the connections on the bottom for burnt or loose wires.
Sorry so long winded, but that is why electronic guys get so much per hour.
30+years working on DOD long range mobile radars.
