I thought i was onto a solution with egift cards but they cant be redeemed via the Appointments Online Booking Site. Ideally the calendar would show the appointment is prepaid (with number of visits but this doesn't look possible either). Its a reasonable issue for us to move over to 'Appointments'.
Unfortunately it seems gift cards with square run in a separate system from what we can tell. We often use gift cards as give aways / sponsorships (helps us track what’s floating around out there and verify someone walking in to redeem). Whilst it may not be ideal for your business, my approach would be to get your customers to bring their gift card with them and each visit you just pay the booking from the gift card to clear balance. You could promote it more as a ‘session package’ redeemable after each visit as opposed to prepaying their sessions. I appreciate this might be time involved too, but I can’t think of another work around on Square for this.