Thunderbird Schematics

Standard Thunderbird wiring​

Most two pickup Thunderbirds come from the factory wired VVT (volume-volume-tone). The exact wiring may vary slightly, but it's basically the same. Most models will use 250k pots (most of us prefer audio taper). Tone capacitors (caps) vary somewhat, but either .022uF or .047uF is a good place to start. Large caps bleed more volume and treble; smaller caps bleed less.
The following is from https://www.axekool.com/gibson-epiphone-thunderbird-bass-wiring-diagram-fitting-instructions/ .

A single pickup Thunderbird would be similar, just less the middle volume pot and pickup.
Presumably the cap is .047uF. Some Thunderbirds came with two .022uF caps in Parallel, which is .044uF . I doubt even Eric Johnson would detect the difference between .044 and .047 . Certainly the rest of us won't.

Bicentennial Thunderbird wiring​

The Bicentennial Thunderbird wiring should look like the following diagram. The pots are allegedly 100k, which is a low value for Gibson humbuckers. Diagram courtesy @GBassNorth .

Three pickup with individual volume and tone Thunderbird wiring​

@GBassNorth has also provided a diagram for building a three pickup Thunderbird with (or modifying a custom shop three pickup bird to have) volume and tone on each pickup.

Standard Thunderbird plus mudbucker wiring​

Also courtesy of @GBassNorth we have a diagram for adding a mudbucker (and selector switch) to any standard two pickup Thunderbird (in this case a Goth). Please note that this is an early Gibson (or equivalent) mudbucker. Epiphone made similar looking pickups they called mudbuckers, but with much lower impedance and Output. Those would need different value components to work well in this circuit.
You could leave out either or both switches if desired (to replace the three way switch, just solder the three wires together that form a W above the switch. The ground connection goes away with the switch. You will have more tonal variety with the 3 way switch, though.