Video #2 credits this dance to Tony Slinger.

Different versions of this dance exist.

Instructions on the  <<http://www.callanishmusic.com/upfiles/The%20Witches%20Reel.pdf|Callanish website>> suggest the women should thread the needle before the men in bars 17-24.
Those on the <<https://www.ceilidhminogue.co.uk/dances.html|ceilidhminogue website>> are a 40 bar version with the men threading the needle before the women and doing so in bars 1-16 and completely different moves in bars 17-40.

The two videos are 32 bar versions but (mostly) show the men going first. Take your pick!