This is largely a solved problem; consider income tax. You "pay" (withhold) monthly and true-up at the end of the year.

Income tax is withheld on the income. Are you suggesting that we open the door to more taxes being withheld from paychecks?

No - I'm just pointing out that amortization and prepayment of an annual tax bill is largely a solved problem. I was more thinking of a monthly request to pay X.

It is predicated on the motorist estimating their annual mileage; but if there was a simple mechanism to make adjustments based on deviation from the estimate then I can't imagine it would be too bad.

Now find a way to make sure it's actually used for its charter, and you'll be celebrated for centuries.

withhold the tax when you fill up, get a refund at the end of the year.

Monthly tax bill for the year prior?

Seems reasonable, a typical payment cycle. What happens when someone doesn't pay? (This is probably a more general question to payment period)

Apply same laws as council tax and/or not paying road tax