We have a winner.
1. I'm an idealist. - Based off one line, but it's right during the big Chapter 3->4 transition. Sana: Geddoe, you still haven't forgiven [Flame Champion] have you? You never change. You always were an idealist and it encouraged [Flame Champion] to no end. But the fact that you didn't seem to understand him hurt him.
2. With friends in many places. - Geddoe knows the Lizard Clan chief, the information dealer in Caleria, Salome, Sana...
3. So you want to know what my ideals actually are? That's... uh... that's a good question. - I'm not inclined to write off Sana's line, since she would presumably know Geddoe quite well, but Geddoe never actually tells anyone what the ideals were that drove him. It may not even be Wyatt's "Don't get conquered" because we don't even know if Geddoe is a Grasslander.
4. This guy thinks he's my rival? He'll come around to my side eventually if I play my cards right. - Duke wants a rivalry even if Geddoe ignores him. Also, he's one of the rare Suiko III recruits you can permanently screw up.
Unused:
5. I can potentially hit the full trifecta on my enemies- I can freeze them, singe them to ashes, and zap them. Just not normally at once. - Geddoe's got the Freeze skill, and potentially True Lightning & True Fire.
As a side gripe, I'm willing to write it off as "mystery! Potential for more revelations later!" in this case, but yeah, the "No one understands my ideals!" JRPG/anime tragic villain where they never actually bother to explain what their ideals are is really annoying. Being an idealist for no cause in particular is like being a hedonist who doesn't enjoy any activities - it just doesn't work. I think that somewhere along the line some people decided that Idealist == psychotic crusader in bad guys. Sigh.