Not getting the full 12 volts

You may have a dodgy cell - if it's new take it back and they should test it for you

cheers

Josh,

You haven't mentioned how you have wired the camera and monitor up but the only wire that should be connected to the reversing lights is the trigger wire that turns the camera on when reverse is selected.
The wiring in modern vehicles are quite small diameter and not rated to take a heavier current draw.

The power for the monitor should be connected to an accessory circuit rated at 10 amps or so and be preferably connected at the fuse terminal strip. Piggy back fuse holders enable you to "add a circuit" to an existing one with its own fuse. This is much better than using displacement style connectors (eg. Scotch lock) to join into the normal vehicle wiring.

In most cases a scotch lock is probably required to connect into the reversing light cable but they are notorious for poor connections.

I would suggest taking it to an auto elec as the problem could be out of your depth and you have problems with 3 separate circuits.

Josh

If there is a difference between the voltage at the battery terminal and the voltage down the back, even when there is no load applied, suggests that there is a connection that has started to act like a resistor, or the main 12V wire has become resistive due to corrosion etc

Your truck is 20 yrs old (and it has been driven in the ocean, judging by your pic) so that is hardly surprising.

Using your multimeter, start measuring voltages along the wire until you isolate the problem.

Bob