[Jonathan Law Feline Guitars]

I would suggest that we may be overlooking some fairly obvious things here which are popular

The bridge on the guitar looks like it has piezo elements – like a fishman powerbridge, or an LR Baggs piezo equipped tele bridge.

I would suggest that the mini toggle and circuitry on a knob is a piezo buffer circuit and allows switching between magnetic pickups , mix of mag and piezo and piezo on it’s own

Most likely has a special jack that will allow the signal to come out in mono as a mix, or stereo via a RTS cable and have the magnetic output go down one wire and the piezo go down the other

Have you checked the battery for voltage ?

The 4 way switch is likely to be an Oak Grigsby 4 way switch for tye magnetic pickups giving

Bridge

bridge and neck combined in parallel

Neck

Neck and bridge in series

I could be wrong , but that is a popular set of options