There is no general consensus when any scan should be done post treatment. It depends on the doctor, and hospital. NCCN guidelines say a post treatment scan should be done 3-6 months, minus any cancer signs or suspicions, and even that is only for T3, T4 disease, and only in certain head and neck cancers like oropharyngeal, not even oral cancer is mentioned.
All my doctors at several CCC do a PET/CT at 3-6 months post treatment, and 6 months thereafter. I'm sure the time between increases thereafter, but I never made it to that point. What guideline this is from, I don't know, maybe it was an old NCCN guideline, but seems many follow this or similar. Some doctors don't believe it post treatment scanning or want to subject the patient to more radiation with no added benefit.
There are other guidelines, ENT's, MO, RO follow, that are followed, and NCCN guidelines list similar too. Like the first year is every 1-3 months, where ENT's they do a palpable, visual exam, and maybe a flex scope. Some say the visual, and palpable exam is just as good ad any scan, but also read in other abstracts a PET/CT is like 28%, don't quote exact figures, in finding cancer than a palpable exam. A chest x-ray should be done yearly, as well as TSH levels for thyroid dysfunction, which may increase as time goes by.
A patient can also be vigilant in doing their own observations, exams. I found all my nodal cancers (8) in the cervical neck, then confirmed by FNA, PET, except my last one, which is probably due to a pec flap, and was told before, scanning is the only way now to probably detect cancer, and was.
Good luck.