Five steps, start to finish: nothing your reception desk isn't already doing, just with visibility patients can actually see.
A patient calls the clinic. Your receptionist enters the appointment. Nothing changes for them.
The moment they're booked, they get a message with their token number, the doctor's name and time, and a private link to check the live queue before they leave home.
They walk up and give their name. Your receptionist searches it, taps "arrived." That's the only new step, and it takes less time than the register.
Their link and the waiting-room screen both show the same truth: who's being served right now, who's next, and where their own token sits, no invented countdown.
If the doctor taps "running late," every waiting patient is updated at once. No one has to walk in and ask.