UPDATE:
I was able to replace my marker lamps finally. The following is true:
If you're talking about the turn signal light box. There are two threaded studs that the ears fit over. Then you screw nuts over the threads to hold it in place.
Unfortunately, one of the mounts had broken off at some point in the car's life, and some Goober deciced to try holding the light in place with caulk, or glue, or snot, or something. I ended up having to pull the facia off enough to replace the CARRIAGE BOLT. These are the bolts with a rounded off head, and a square shoulder to fit in the square hole in the bumper.
Sorry, I don't remember what size I bought, but they were only a few cents at the hardware store.