How do I find tempered monsters?

I've unlocked tempered monsters and I occasionally follow tracks for them, but they never seem to end up with tempered monsters while on expeditions. Do you only find tempered monsters on investigations/quests or can they also be found during expeditions?

Following tracks of tempered monsters doesn't lead you to them, it unlocks tempered investigations (though I don't think this is guaranteed).

I believe that aside from assigned/optional quests that have tempered target monsters, these investigations are the only way to find/hunt tempered monsters; they will not just show up on an expedition or other quest.