First of all, you got that wrong, Yamoshi isn't exactly the first SSG, his spirit was with the first SSG (ritual), he was dead already when the first SSG was born.
This doesn't matter since the actual Yamoshi fought evil saiyans until he was killed as well but that only proves again that you got the story wrong. It's not that complicated you know
Second, that's not how reincarnation works. You can only reincarnate if you are evil (you are send to Hell, they punish you and then you are purified and reincarnated), good people just lives in the Heaven and Toriyama confirmed that his spirit is free too (when he explained how he helps for the SSG ritual and how he meet Namek's great elder) so no, no reincarnations for Yamoshi, Yamoshi will live forever as a ghost