This must be covered here already but I can't find the post so here goes [again]. The W124 has two modes of bulb warning -
on fault wherein the warning illuminates when the bulb should be on but isn't, and
latched wherein the warning light stays illuminated from the moment a brake bulb is sensed to have failed until you turn off the engine. One cause of bulb failure warning after confirming all the bulbs are good is weak clips in the tail light covers/bulb holders.
These two pictures show the plastic tab separating from the metal strip that holds the bulbs in the area by the brake bulb where the strip bends towards the side marker. Note how the plastic flange with a tab that should retain the metal strip has deformed pulling the tab away from the metal strip -
This picture shows the plastic tab separating from the metal strip that holds the bulbs in the area of the reverse bulb. The tab still contacts the metal strip but the plastic flange is deforming -
Sadly, we come to a cliffhanger. I don't know how to fix this other than replacing the tail light covers/bulb holders (later models might have less flexible plastic) or creative use of clamps. You can bend the bulb contacts but that only lasts so long.
It could be other things. My '87 SDL would throw a bulb failure warning going over railroad tracks. I pulled the bulb warning relay to make sure it was properly seated and heard a rattle. I replaced it with a relay that didn't rattle and it only threw a warning when a bulb was out.
Sixto
83 300SD