I replaced one of my TinyTach's internal batteries with an external battery pack using two AA alkaline batteries in series. Been going several years so far, but if the AA batts die, easy to replace them.
This post also reminded me of our issues with TinyTachs on DE Stubby and LEU Treehugger. I found my write-up and several other posts on TinyTach and similar units at ----> https://www.eaglersnest.com/forum/index.php?topic=1885.msg12771#msg12771
On Stubby, I finally replaced the gas type TinyTach with a diesel type electronic tach (not a TinyTach unit, but don't know mfg, from ebay, $15). It uses a magnet attached to the prop hub, and has a sensor that is mounted to pick up the rotating magnet. It has an internal battery. So far, it works flawlessly.