The moment to book the next appointment is while they are still sitting there, happy with the result. Once they have left, rebooking depends on them remembering, choosing a date and getting round to it, and a large share of them will not — not because they were unhappy but because life intervened.
Make it a habit rather than a decision, and make it specific. 'You will want this again in six weeks, so that is the third — morning or afternoon?' A concrete choice is answered; 'let me know when you want to come back' is not.
Tie the interval to the work rather than to a policy. Regrowth, fill, treatment cycle — the client can see the logic, and the logic is what makes the booking feel like advice instead of a sale.
If they will not commit to a date, do the next best thing: agree that you will remind them at the right time, and set it. A reminder at six weeks from somebody they already like converts far better than a marketing message to everybody.
This is also what protects your best slots. Evenings and Saturdays get taken weeks ahead, and the client in the chair is the one with first refusal. Regulars who rebook every visit keep their slot; regulars who do not, lose it and then feel let down.