This image shows a 7.2V NiCad battery (for a Technophone TP2 brick phone - date stamp 1991) powering a cheap Bluetooth audio module (the silver square with the blue LED), with a little help from an Elegoo voltage step-down converter that came with an Arduino kit.

If I can fit the circuitry on the left into a Technophone TP2 case (possibly using a smaller breadboard!) and connect up the battery then I should be able to make a working Bluetooth headset of some kind.

It would be even better if I were able to keep the original circuitry (except the redundant analogue '1G' RF board) inside the phone, so that I can power up the phone and charge the battery as originally intended with the new Bluetooth bits inside.