I've read your post a few times, but I can't figure out what could be causing it.
Are they the stock foglights or aftermarket? Does it look like anyone tampered with the wiring?
I'm not sure if a relay is involved, but if there is, maybe it's stuck in the open or closed position.
I would honestly have a professional take a look at it, maybe even the dealer (I hate suggesting that but it might be your best bet)
'94 Supercharged E36 325is (150,000 original km's)
-Vortech V9 G-Trim @ ~10psi w/ BOV
-255LPH Walbro fuel pump
-TEIN SS Coilovers w/ Pillowball mounts
-Keskin KT1 17x8.5 & 17x10
-Remus full catback
-Authentic Rieger Infinity I body kit
-SMT6 EMS (Untuned)