I'd say an Adventurer's Strange Mood (Wanderlust?) should afflict anyone, perhaps taking their not-traditionally-moodable skills into account (Plant Gatherer goes out on a botanical hunt, to return with something new, or else now able to add knowledge of a previously unfarmable plant into the pantheon of horticulture; a Geographer (Scholar) might come back with
very detailed knowledge of some other site, either directly useful or adding to the success-rate of a later Mission (but not
itself produce a Raid/Exploration/etc result such as retrieved captives or artefacts).
I'm inclined to say an obvious Military Strange Mood (or its successor) should indeed be an on-map process developing a new attacking
or defending style (effectively a weapon/armour skill bonus, pass-onable by training by one who has acquired its mastery). But I can imagine Ambusher(/Sneaking) moodable taking advantage of an off-map adventure (becoming 'one with nature', so long as they can overcome the fear of turning into an elf) or the Observer skill (sitting still and comprehending more of the surrounds, making more suitable for lookout duties) or Tracking one (the dynamic alternative, assessing the movements of (a) specified individual(s) of prey or thief/kidnapper or other foe).
How prescriptive should this be? Well, with the disappearance of Moods as we know it and mumble-mumble-mumble-Spheres being developed up, it may be a bit different and
capable of being different. Some 'traditional' transitions from journeyman to craftsman by a suddenly masterful application of a production skill, some innovate or revelate in more intangible ways. I could even imagine a (version of) Military Mood coming up with an idea for a new piece of equipment (I'm sure I've been involved in this discussion, but a quick look for
Procedural Weapons gives something I
wasn't involved in) which needs documenting (in-game scribing or other information-passing) then is added to the Forge options. Pinch/repurpose some of the newer worldgen instrument-defining code for this, perhaps? Either as a worldgen's "potential future discovery"(/ies, as a list) or as a wacky createNewItemClass()-ish sort of thong at mood-time. (It might be an option for a weaponsmith/armourer mood-type-thing, but I like the idea that a warrior would come up with the thought "you know, if I had a sword-gauntlet/knee-hammer/turtle-like-back-shield, it would solve <problem>...")
But this is all out-there-speculation, a little aimless and a lot straying beyond the direct focus of the thread.