You need to get a Volt meter or test light.
And just FYI, most people do not notice when passenger side reverse light burns out, and do notice when drivers side goes out.....
So if passenger light was already out and now drivers side is out you may be over thinking it, could just be burnt out bulbs
Block the tires
turn key on
remove transmission Reverse switch connector and test wires for 12volts, ground meter or test light to trans, only 1 wire will have 12volts and only with key on.
If you get the 12volts on 1 wire then power is getting there, other wire goes to reverse lights.
Now remove back light assembly and then reverse bulb
With key on, trans in reverse, and switch hooked back up, see if you have 12volts on the center connector of reverse light socket, ground to bumper or frame.
If you have 12volts then move ground to socket metal case, if no 12volt then ground is bad, you will need to trace it under truck to the frame.
Also if you have a trailer light wire it may have reverse light wire and this can effect reverse lights if connector gets corroded.