Automatic? My reverse lights wouldn't work because someone removed, and never replaced, my backup light switch on the trans housing (4spd manual). And UConn is right. Good grounds are so important. Something I found (the hard way, duh) is when you remove a ground and paint under it, then replace with new hardware, could lose ground contact. Run a wire direct to your neg battery terminal to the ground on your lights. At least you'll rule out, or confirm, a ground issue.
Most of the time it's a grounding issue. 1st think I would recommend is to upgrade the lighting. The wiring for the lights on these cars suck. I will convert mine to LED with new sockets. Your grounding issue will go away as a result of your upgrade. Make sure the mounting plate is clean when you plug in the socket.
If you intend to keep the old for now I would suggest the following:
1. Install ground terminal block. Mount somewhere in trunk and ground it to a good connection on the frame. 2. Clean your all ground contacts 3. Run grounding wire from terminal block to ground contacts
For example, on your rear tail light harness there is a ground wire that comes out of the harness and is screwed into the frame. Connect your grounding wire from the harness to the ground terminal block. Do this for anything that you feel might not be getting a good ground.
Engine Test Stand Playlist: https://www.youtube.com/playlist?list=PLwoxyUwptUcdqEb-o2ArqyiUaHW0G_C88 restoring my 1968 Firebird 400 HO convertible (Firedawg) 1965 Pontiac Catalina Safari Wagon 389 TriPower (Catwagon) 1999 JD AWS LX Lawn tractor 17hp (my daily driver) 2006 Sequoia 2017 Murano (wife's car) 202? Electric car 203? 68 Firebird /w electric engine 2007 Bayliner 175 runabout /w 3.0L Mercuiser__________________________________________________________