But an individual Clan Wolf warrior could challenge an individual Sea Fox warrior, or vice versa? To what extent do superiors have to approve that sort of thing?
I don't particularly care what the Trial is about, as long as it makes sense.
In terms of the glory, my understanding is that it depends on what you're fighting over, who you beat and what their bid was, how you beat them and what your bid was, and how closely you adhere to Zell.
Well, stepping back from what the trial is about then...
I see two basic rationales for a 1v1 duel: A- a Trial prosecuted between Clans that simply got cut down to 1 point per side, and each side shows up with a single mech & mechwarrior. B- A grievance of some sort between two individuals. I'm going to presume you're angling for more of a B scenario.
So, two mechwarriors having a disagreement and settling it from their respective cockpits can be done with or without sanction by their respective superiors. It could even be sanctioned for one mechwarrior but not the other, for that matter.
Ideas for why a 1v1 duel might happen with or without sanction:
Cultural Importance (the entire Bloodright example I discussed upthread)
The warrior in question is an officer trusted to command forces necessary to launch raids (borderline/blurring with case A rather than being a case B)
Perhaps no interstellar travel is necessary; there could be infinite reasons why an enclave exists or a delegation is present on the same world with the rival Clan's garrison. Proximity allows for the possibility of two pilots getting into a disagreement about any old thing and running to their respective hangars to come back and settle it "like warriors".
Perhaps the forces are on the same world together as part of a larger Trial of Possession/raid. Perhaps the conduct of one mechwarrior was called out as "dezgra" by the other, and their respective commanders permit the two to conduct an immediate Trial of Grievance over the matter after the ToP is concluded but before the invading force returns home.
et cetera. Lots of possibilities.