Great to hear that you're learning quickly (and enjoying it too!) @cappers.I'd forgotten about this question I asked in April.
Three months later I wonder how I could have been so dumbStuff that seemed so complex and alien is slowly becoming second nature.
I'm finding this a bizarre and wonderful journey.
FWIW this is in no way a 'dumb question'! At the bi-annual series of 10 'jazz improv. workshops' that I've joined in with 5 times now, participants always ask your initial question. Mainly those that participate for the 1st time. But also those who've just 'forgotten' what the clues are.
Because these workshops are focused on improv, the chords are written out, even on the 'melody sheets'. I should add that many (amateur) sax/trumpet/clarinet players are mostly used to just playing the 'notes as written'. So thinking in terms of chords/scales (major or minor) when learning to improvise is often 'challenging' for them. So the main question thy ask is always 'yes, but if the chords weren't written, how would I know from the key signature whether it's in a major or relative minor key?'
As previous posts indicate, our workshop leader always tells participants to:
- learn the common major and relative minor scales
- look at the beginning and especially the end of pieces; the endings often resolve into the 'tonic' (i.e. a 'C' or an 'A')
But again, your ears (or your eyes by scanning will tell you whether a melody is in a major or relative minor key.

Stuff that seemed so complex and alien is slowly becoming second nature.