See my earlier comments concerning the third movement of a mozart or haydn symphony.

A "dance" can be a musical form as well as a piece of music written for dancing to or it can be a series of choreographed movements.

Which came first - dancing or music?

Maybe chanting and dancing simultaneously without a divide between dancers and musicians?

Who knows - who cares.

Both art forms can exist independantly of each other.

What do you call a tune from Ireland with two or three parts in the dorian or mixolydian mode at a moderate to fast tempo in either 9/8 time or swung 3/4 time (depending on how you hear it)

I'd save time by calling it a slip jig.

We could try to construct a logical hypothetical view about whether music or dance came first, but jigs and reels came into existence long after that time, so there is no telling whether musicians invented them first and dancers were inspired to get up and follow the music, or whether dancers requested music that fitted the rhythm of their dance.

All you can do is do the research and find the earliest reference to jigs and reels as dances or as musical forms and even that is unlikely to be conclusive since the tradition was passed largely from musician to musician and from dancer to dancer.