When, and how frequently are moderator elections held on law.SE?
Can users nominate anyone for moderator other than themselves?
I asked some related questions on Meta.SE many years ago:
You can see that people at Meta.SE (who are mostly not active on Law.SE) are strongly against the idea of having elections every few years, and they would rather have elected people remain in power until they die or resign or get kicked out (extremely rarely).
For a site like Law.SE, in which a "graduation" election has already taken place, elections only happen when it's decided that it's desired, which would usually happen in the following circumstances:
If the number of diamond moderators goes below 3 (due to a death, resignation, or rare removal), then often (but not always), Stack Exchange employees will schedule an election within a few years, at a seemingly arbitrary time (they usually notify the existing diamond moderators but the rest of the community is usually left in the dark).
If the workload becomes too big for the existing diamond moderators, they can request for the Stack Exchange employees to approve adding more of them. These new diamond moderators would usually be chosen via an election (though in rare circumstances they are appointed by the SE employees).
A third possibility, which I haven't seen actually happen in the SE network, would be for the site's community to ask for it on the site's Meta, and for there to be overwhelming community support. For example if you felt that an election should occur, you could write a Meta post explaining your reasoning, and if the majority of the site's Meta participants agreed with you, perhaps an election would occur (I've never seen it happen this way though).
In all three of these cases, the Stack Exchange employees (not us) make the final decision about whether or not to have an election, and this is decided unilaterally by them, or by request from the existing diamond moderators (I haven't seen the third option happen, in which the non-diamond community members were the driving force behind the decision).
How often does this occur? Rarely. Since the initial "graduation" crew were elected in 2016, there has been 1 election.
Only users that nominate themselves are listed as candidates in the election. You can make suggestions, but they will not appear on the ballot card unless the users that you suggest decide to complete a nomination form on their own.
I believe that elections are generally held only when the staff thinks that a site is in need of additional moderators, usually because one or more existing mods have resigned or become less active, or because traffic has increased. If moderation issues are being handled in a timely way without over-straining current mods, there may be no election for years.
I believe that users can publicly suggest that a certain user run, but a user must self-nominate to be on the ballot.