Do they not make heated gloves powered by the same ubiquitous rechargeable battery pack as used by heated waistcoats and gillets?
No reliance on the bike's system at all, then.
They do Rex. Here's a pair. 7.4v lithium-polymer jobbies, rechargeable, they say, up to 200 times. Sadly, my ones (Paragon thermotech, from RST) died young - one shorted out somewhere inside and burnt me. I have been playing with them of late because it's been chilly and bought new batteries, all the way from China via Germany, but they don't seem to want to co-operate despite the light displays seeming to work. Expensive when I bought them a few years back, so although they were great when they worked . . .
By contrast, have been mighty impressed with Hot Hands from Oxford (1/4 the price of the gloves, and Black Sheep's are far less than that), which have worked for over 10 years. Yes, they consume about 34W, 3A at 12v, but my A10 supported them fine, with a pre-LED-days 36W halogen up front, and my old AMCs with dynamos (and LEDs now) support them, no big deal. Easily transferable between bikes if not wired in too 'deeply', and comfortable under the hands.
I'd like both warmers to work, obviously, but shan't be spending those £$€ again on heated gloves. Over which over-mitts shouldn't be worn (my instructions said), which is a downer for water-proofing as 100% all-day waterproof gloves are hens' teeth.