Yep - there are 2 sets of wires going through the '67 neutral switch. Purple/purple for the neutral safety and pink/bright green for the backup lights.
It very well could be the whole switch would be defective taking out both the backup lights and the neutral start feature. That's what I meant by 'check the switch' as in put the shifter in neutral and try and and start the car.
If it is the switch - I got a nice reproduction for the TH 400 from Rick's Camaros. My switch had been removed and the console wiring harness wires jumpered so the previous owner could start the car. So not only did I have to replace the switch, but the console harness too. Thanks, whoever you were!
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