I will tackle one piece of this. I will bet you that your neutral safety switch (which also signals you are in reverse) is broken or missing.
I know there is a ground wire for the rear light harness that I think screws to the reinforcement panel that surrounds the gas tank inlet inside the trunk. Without it grounded - you are going to have problems.
That harness also has the wire to the rear license plate light and gas tank sender.
Sounds like you may need to replace the entire rear light harness.
2012 Mustang Boss 302 #1918, Competition Orange. FGF replacement 2006 Mustang V6 Pony, Vista Blue. Factory ordered. 2019 BMW X3 (Titled to the wife, but I'm always driving it for her. So I'm claiming it) Old projects, gone but not forgotten: 1967 FB 400, original CA car. After 22 years of work, trashed by the guy who was supposed to paint it. I had to sell it. 1980 Turbo Trans Am 1970 Mustang fastback, 351C 4Bbl, auto 1988 Mustang GT, 5 speed 1983 F-150 4x4, built 302 1994 Chevy K2500 HD 4x4, 454 TBI
