AnnieB, that helps a lot! You make it sound simple, but I was having a brain drain on this. I thank you for the delineation between maintenance (the adulting that I have to do!), vs. emergencies, this clears up many items!
Things that fall under sinking funds:
Car maintenance, routine medical expenses (eye glasses, contacts, hearing aids, medical copays), insurances that bill quarterly, semiannually, or annually. Take the dollar amount and divide by the number of months for long term things. Add these totals up and save. I would throw a few medical copays in there (if you have copays) because who doesn't get sick or need a prescription as a result?
For high deductible insurance, you could put money in there and/or take advantage of your company's HSA. You just need to know the rules of using vs losing the funds. That is something you would take up with your HR Department.
You CAN cap sinking funds. Once you have your high deductible insurance in there, you would no longer contribute to that unless the limits changed or you used the funds.