This is about the best article you could hope for on the question of EAB logbook entries.

https://www.kitplanes.com/aircraft-r...-and-logbooks/

Aside from some specifically required entries, it sounds like there's a lot of this that's open to interpretation. I could swear I was told that EAB logbooks didn't require any entries other than the ones specifically called out in the regs, such as the annual conditional inspection, major mods or repairs, and some equipment stuff. Since anyone can do maintenance on an EAB, I'm not sure anyone really needs to "sign it off". I'd put anything significant in there just for a proper maintenance record, but I'm not convinced you're legally required to.

As for the original question, if you want the gearbox inspection done in a way that gives you full confidence, I'd stick with one of the big service centers. Rotax seems to make it difficult to find those, but Lockwood, LEAF, South MS Light Sport, Roger Lee's shop, etc. I'm sure there are many more.

Rusty