A1016 wireless keyboard can't/won't pair with original or any other computer

I had two A1016 keyboards - one that didn't register the left Alt key due to a corroded membrane thanks to a coffee spill, and one that was very yellowed due to exposure to sunlight. I've cleaned and reassembled the best of the two, so now (in theory) I have a fully functioning immaculate keyboard (electronics and membrane that have never seen liquids, case that has hardly seen sunlight). It didn't want to pair with my iMac (10.9.5), but did connect to and worked fine with the G4 Mac Mini (10.4.11) it was originally paired with. After un-pairing from the Mini, it now won't pair with anything:

10.4 sees it, offers an 8-digit passkey and always reports "The pairing was unsuccessful. Make sure you are entering the proper passkey..."

iMac says "Too many pairing attempts. please reset the device"

As a final attempt, I tried connecting to a Macbook Air that had never seen the keyboard before. It offers a 6-digit passkey and then says "Passkey entered did not match".

I've tried using the numeric keypad and top-row, and both Enter and Return, in case that difference mattered.

This is the original transparent and white keyboard, so the common instructions for un-pairing from the keyboard don't apply (power on and keep the button pressed). I've tried variations on that (power on with 'Esc' or 'Eject' pressed), but with no success.

I have searched thoroughly for "a1016 reset", "too many pairing attempts" and so on, but found nothing that makes a difference.

To boil all of the above down to a single question, I'd ask is it possible to do a "factory reset" on an A1016 keyboard?