I just put an aftermarket stereo in my 86 caprice and I lost my dash lights and tail lights and keep blowing the fuse for the tail lights when I installed my stereo my dash light did not come on and then I noticed that my tail lights did not work either so I checked the fuse and replaced it and as soon as I turned on my lights I blew the fuse
Sounds like you used the tail light wire in the radio's harness for the new radio's ground wire. You can prove that by unplugging the new radio and replacing the fuse. The tail light wire at the radio is to tell the display to dim when you turn on the running lights. There's another wire from the dash light circuit to tell the display how much to dim.
The dash light circuit is a sub branch of the tail light circuit, so when the tail light fuse blows, the dash lights won't work either.