A friend of mine who is a student of US politics told me that in the event of a post-election presidential death, one possibility was that the Vice-President, on becoming President, would appoint the President-Elect as VP, and then resign 24 hours later, allowing the new guy to take control straight away. I can’t remember if this was an informal agreement that the parties had discussed, or just a suggestion by some politicals professor, but it struck me as a very sensible idea.
Anything like that would be informal. Even if there is an agreement between the two major parties it holds no official weight from a constitutional standpoint. Honestly, from the Constitution’s point of view political parties don’t exist.
So it might be a gentlemen’s agreement, but no one is bound to it.
This is brilliantly ironic given the near impossibility of any other party or independent ever getting a sniff of power.