Being an active participant has nothing to do with providing recurring services. For example, say I pay a property management company to take care of my rental for me, and that company makes decisions about who the property is rented to and for how long, They also take care of any repairs and upkeep that needs to be done, as well as providing recurring services to my short term AirB&B rentals. That does not make me an active participant. But I do provide recurring services. That's what I pay the management company for. Realize that there is a difference between "performing" those recurring services, and "providing" those services. I pay the management company to perform them. Therefore I provide them.
Now for days rented, vacant periods between renters counts as days rented provided you did not live in the property or utilize it for personal use for even one single day between renters. The property remains business use. So if you had say, a total of 45 days vacant in the tax year, the property was still classified as rental property/business use. So your days rented would be "the whole year".
This is why, if the setup qualifies, you would report this on SCH C just like a hotel does. When a hotel has a room sit empty for weeks on end, that does not change the fact that it's still business use property and there is no personal use days.
When you claim personal use days, that not only affects the mortgage interest. It also reduces the property taxes and insurance that is deductible on the SCH E or SCH C. As you know, the difference goes on SCH A. Then until the SCH A deductions exceed your standard deduction, those itemized SCH A deductions have absolutely no impact on your tax liability.
