Just wonder how you "know" there is power to the reverse lights but you don't know where the swich is.
Might be handy to confirm which transmission (auto or manual) is in your car. I'm going to assume it's a manual.
For late model manual Mustangs, the manual reverse switch is on the transmission. For example on a 95-98 MY there should be power to transmission reverse P/O wire with the key on. If not, STOP and check the #1 I/P fuse.
Shorting the P/O and BK/PK wire should force the back up lights to come on.
Disconnect the reverse switch. Measure the resistance through the switch. It should be high (open) when not in reverse. Should be low (closed) in reverse.
For the automatic transmission, the wire colors are the same (P/O and BK/PK). However the reverse circuit goes through the transmission range selector (TR or DTR). Which is accessed from under the car.
The automatic neutral safety is R/LB and W/PK.