An '03 "5 speed" could be a manual or automatic, M5OD or 5R44E
Which is it?
Manual will work fine for any year as long as it is from/for an 3.0l Vulcan engine
Reverse wiring is just a contact closure switch on drivers side of trans, toward the top, same on any manual trans, connector might be different
Automatics use a linkage switch for Reverse lights, '94 used NSS(plunger type switch), '03 used DTR sensor on the shift rod of trans
Reverse light switch gets power with key on
When trans is in Reverse the switch is closed and power is sent down the other wire to the Bulbs in the rear
No relays or other "modern" complications in a 1994 Ranger
Just wires, fuses and mechanical switches, nothing is hidden
For 1994 Ranger, in cab fuse panel #13 is 10amp fuse for dash lights
This fuse is powered by main light switch also goes thru Dimmer first
So if #13 fuse is OK then problem is most likely main light switch connection or dimmer, either could be worn out after 24 years, but test them
Also in cab fuse box #10, 15amp, is Brake light and park light fuse
If front Park lights work, and 3rd brake light on cab works, then I would look at the GROUND for the rear lights, brakes and tail lights, AND Reverse lights all share the same ground
Brown wires are the Parking light wires
Light Green the Brake lights
Black are the Ground wires
Park and Brake use same Dual Filament Bulb socket, so bad ground would disable both
Turn signals, in Rear, use separate bulb but share same Ground as Brake and Park lights
If trailer light wiring has been added check that first
Get volt meter and start to test voltages and Grounds