You are absolutely right about the light monitor has no influence on your defective tail light.

The system is not powered at all. The monitor system is simply a set of fibre optics transmitting the light from the taillights to the "snake head" shaped light monitor on top of the rear seat (should be fastened to the back of rear seat with two small screws) allowing you to check that your tail lights are actually functional just by checking you rear view mirror. There would even be a set of light monitors on each of your front fenders for the headlights. Those will have three indicators on each fender. One indicator for the park/indicator lamp and one for each headlamp. The brilliant part about this system is that what you see is the light from the actual light bulb transmitted to the monitor via the fibre optics. Hence it is not dependent of the electric system, like on modern cars.
Here is an article about light monitors.
http://automotivemileposts.com/autobrevity/lampmonitor.html
If your upholstery shop has forgotten to reattach your lamp monitor on the rear seat, you need to remove the seat cushion (push it backward and upward. A no-tool operation). Then the rear seat back can be removed by unscrewing the seat belt retractors. They are secured with a Tx 45 or Tx 50 bolts. Once they are out, the seat back can be pushed upward releasing it from three hooks securing the upper part. Once you have done it once, its very easy. Your cab being a convertible will give you plenty of space for the operation too

If you don't find the lamp monitor behind the seat, look for the fibre optic cables. If they are not cut, you can buy a replacement monitor with one of my friends who 3D print them.
Enjoy