In American Square dancing Taw means a guy's partner.

One version of the Dance Sally Gooden goes like this.

Number one go bow and swing
the gent goes out to the left of the ring and
swing Sally Gooden with a right hand 'round
and now your Taw with a left hand 'round
Now the girl from Arkinsaw (right hand lady) with a right hand 'round
and now your Taw with a left hand 'round
across the hall and swing Grandmaw with a right hand 'round
and back to your Taw and everybody swing.

This could suggest that the use of the word in square dancing is derived from the meaning of 'starting point'.