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tl;dr: Does being removed as a moderator result in an ineligibility to stand for election? If so, does the ineligibility apply only on the site(s) where the moderator was actually removed/de-modded, or does it apply to all sites?

How does the moderator restoration procedure relate to a former moderator getting elected or re-elected by a community? I asked this a while back and never got an official answer.

The moderator reinstatement process seems to indicate that a favorable result for the former moderator results in immediate restoration of their diamond, without any need for an election or even any community involvement at all. Is this intended to imply that the former moderator may alternately choose to seek restoration by being elected or re-elected by one of the Stack Exchange communities, or is it intended as the sole restoration process and/or a prerequisite for becoming an election candidate?

This answer asks specifically about a former moderator seeking election on the community that they formerly moderated, but there's also the possibility that such a person might seek election elsewhere. The Initiation section of the restoration process states:

Previous moderators (PM) may request reinstatement through the /contact form on the site that they wish to be reinstated....

Thus, it isn't clear if this reinstatement procedure even applies to a moderator seeking election in another community. What happens in that case? For example, suppose I was dismissed as a moderator for cause from Shoes and Ships Stack Exchange. I contribute quietly for a sufficiently long period of time (e.g. at least a year, to allow any possible general site suspension-related bars to expire), eventually deciding to leave my old haunt alone and instead seek moderatorship on Sealing Wax.SE, which I have never moderated before. What happens in that case?

  • Do I have to seek reinstatement on Shoes and Ships.SE before I can stand for election on Sealing Wax.SE?
  • May I just go ahead and run, letting the community determine if I am worthy?
  • Do I have to apply for "reinstatement" on Sealing Wax.SE despite the fact that I have never actually been a moderator there?
  • Do I have to begin a "generic" reinstatement process that does not give me back my original diamond, but restores my ability to stand for election?