I have a 1973 Cadillac sedan DeVille and I'm having problems with my tail lights, brake lights, reverse lights and signals. I have power coming from all the lights but they still don't work.

yes but the GROUND doesn't...you must trace the black battery cable to where it attaches to the frame/ground...disassemble and wirebrush the lug (use a pliers to hold to avoid damage) and the chassis too....till shiny and comfortable with a 300 cold cranking amps connection (the thing that made it corroded in the first place) ...bulbs will be able to complete the ground circuit...you could verify by using a multi-meter at the black battery terminal, then test the ground will have limited voltage...this is why you must wirebrush them clean~

I had a similar problem in my 60 Buick. It turned out to be badly corroded contacts in the turn signal switch. I was able to take my switch apart and clean it up real good to fix the problem Good Luck, BuzGuy