Thanks again,
@Chip, for instructions to fix this switch.
I finally got a stock Tascam switch, which is, in fact, a Legion SS21 two-pin rocker. The only direct reference I could find to this switch is this
Ebay posting (currently active, I don't know for how long).
Tascam/Teac sold me this switch for a grand total of $10, shipping included. They've now jacked the price to $27.59 for the switch alone, and the new P/N is X612651029.
I won't say it's necessarily worth it to get the switch from them at this price, but it is a perfect fit, and comes with wires and a connector attached. I used no glue to reassemble, it snapped in so nice and tightly.
Long story short, I followed just 2 parts of Chip's instructions. I removed only the bottom plate and the input board with the power jack.
I actually removed the switch before disassembling, by carefully prying it out of its rectangular opening using a couple of very small, flat-headed screwdrivers and an old credit card to use mostly as a base for prying the switch out without marring the casing. The factory glue is tenacious, but I managed to get it out pretty cleanly. The switch's connector actually popped out of the board as I pried the switch out of its opening and then pulled the wires through.
Once I removed the bottom and board, I simply fed the new wire and connector through the opening, attached the connector to the board, reinstalled the board, and finally snapped the new switch into place. Tested things out, then reinstalled the bottom plate. The whole operation took me between 10 and 20 minutes.
I'm linking some pictures, in case they're helpful
Switch,
Switch side 2,
Attached to power board,
Before snapping into place