Where does the reverse lights get their current?  I have nothing at the safety switch.  

Hi If original wire it should be color coded, may be able to trace it back unless it disappears into wiring loom.
 The thunderbirds  have a great wiring manual and is probably the same as regular cars.

On my car the circuit starts on the light switch.   If you have a replacement light switch, they only work with the key on, AND the headlights on.

The power can be hot off the key the wire goes to the switch on the NSS. There is an extra two tangs.   I think posted the accessory wiring schematic a couple years ago. 

You should have power when that comes on and able to power the lights when the shifter is put into reverse.

Thanks guys that saved me some time.