Full disclosure: I've wanted a little green guru on my back, swinging the wisdom bat for 35 years now. I'm also ignorant to any canon details on how long Yoda's been the Grandmaster of the Jedi Order.
That out of the way, with the information we have on Yoda:
- The E5 Yoda who essentially was Star Wars, trying to teach Luke to make decisions with a calm mind and not out of anger or aggression. I think most of us are familiar with this guy. He laughed at the idea of wars making one great and explained that jedi use the force for knowledge and defense, never attack. It's interesting to note that he gets flustered and shuts the conversation down shortly after that (clear your mind of questions).
- 25 years years or so before that, the reverse Yoda in E2 pretty much single-handedly starts the Clone Wars. Most of us are familiar with that guy too (though maybe some of us prefer not to think about it). He almost immediately seems to regret it and very explicitly says it at the end. The level of offense he took at Obi Wan calling it a victory tells me he knew it was a mistake. Yoda becomes a very complicated character to me (in a good way) from that point on through the tv show and the end of the OT.
- Some only-vaguely spoilery stuff from season 6 of TCW, Yoda realizes theres a darkside to himself that he's been ignoring, is aware of Darth Bane as the sith lord that instituted the rule of two and it's emphasized that compassion and self-sacrifice are crucial to survival (certainly for the jedi in particular).
- This leaves us with a lot of interesting plot points and speculation.
Wouldn't a long-lived GM of the Jedi Order give the sith a personality to exploit they couldn't pass up?
How did the jedi become a branch of government?
Yoda made a snap choice against his character to start a war when a large number of his people were at risk. This points to his suppressed darkside to me, especially since he facepalms himself so hard.
I can't avoid the connection to Yoda's species because with what's out there right now, it's a pretty compelling story waiting to happen. I'm not suggesting a movie that shows something tragic actually happening to his people (I'm a fan of the mystery-species trope) but there's potentially a lot of time after that to show how Yoda thinks he deals with it but instead suppresses it.
There's a ton of opportunity to explore the sith connection to his species' disappearance, Yoda's awareness of the sith lineage, jedi enmeshment by the Republic (plus the bonus Tarkin revealed real estate choice. If that was Yoda's influence it would certainly be mythologically relevant).