I paid $20 for a remote page turner on Amazon and the battery lasts weeks. There’s no Bluetooth involved, it just uses basic radio signals to trigger a pulse that the kindle interprets as haptic input.

It’s one of my favorite purchases, because now I can actually fall asleep while reading the kindle since I’m not activating my arm muscles to turn every page.

This is the item (my kindle is one of the earliest versions, from 2011, if that matters): https://amzn.eu/d/aJaesjd