Ok, so now that the why Dunkelzahn died is out of the way. Why go through all the trouble to become President in the first place? Was that a last minute decision or had he put things in motion by selecting who'd succeed him?
This is just a guess since there's no canon explanation given (and likely not one to come), but here are a few reasons he may have run for president while planning suicide:
1. He hoped he wouldn't need to off himself because the warnings he'd given the others in the know back in the Aztlan sourcebook.
2. He really wanted to be president to help guide the country similar to the sort of bequests he made in his will to prepare the world for the Horrors (check out Ancient History's Annotated Will on the link above).
3. He wanted to make sure that no one else won the presidential election except his hand-chosen man, Haeffner.
4. He wanted to make sure that he was elected president before he died, giving his will as much legal clout as possible since any challenges to his citizenship (and thus his will) would've been made before he ran.
5. He knew a rift would develop when he offed himself and that rift would eventually allow his brother Ghostwalker to return, and the only way to ensure he would be in the right place at the right time would be on inauguration night.
That's just off the top of my head, it's probably all of these and twenty more reasons we'd never be able to figure out.