I did have a hyper-T cat, but it has been a few years and I'm in Ohio.
Initially, you're trying to establish a dose that gets the thyroid levels down enough that the cat is stable and not at risk of heart attack, etc. You may need to recheck more frequently during the dose adjustment phase. Once you've got a workable dose, I believe Emmy was checked every 6 months, unless something seemed off.
If the cat is under 15 and in otherwise good health, you may want to consider I-131 treatment as it will ablate the excess thyroid tissue. It is expensive up front, but compare that cost to the cost of at least 2 blood draws a year, daily methimazole (Tapazole) dosing which may need compounding if you want to rub it into the ear instead of straight pilling for the number of years you estimate your cat may continue living. With diligent dosing, Emmy went 5 years before the methimazole dose needed to control her symptoms was high enough to generate adverse effects (diarrhea in her case).
Also note that in senior cats, hyper-T may mask symptoms of renal failure; when you start treating the Hyper-T, you need to be vigilant for signs of that and pro-active it treating it - pick the low phosphorus AND low carb foods.