Only the people you invite. Your 12 weeks per year are yours — full stop. You can use them yourself, send your family, lend nights to friends, or let them sit empty if you want. No other owner can book your allocated nights, and GoForth will never rent out your time without your explicit permission.
If you do want to earn income on nights you won't use, GoForth can coordinate short-term rental placement on your behalf. But that's entirely opt-in, owner by owner. Your nights are your nights. Think of your 1/4 interest like your own apartment in the building — nobody walks in without your say-so.