[1998 Brickyard]

Definitely a battery tender.
I have one that stays on board the convertible. It is permanently mounted beside the battery.
The parasitic milli-amp drainage from radio memory, ECU, etc. will drain a battery enough not to start the car within a couple of weeks.
I change the oil in the spring due to possible condensation in the motor.
I add Sta-Bil to the fuel tank when I put a half tank at the end of the season.
I also go for a drive for about 1/2 hour or longer 3 or 4 times when the roads are really dry. I think that minimizes the flat spots on the tires.
I cover it up with a good cover.

I like the idea of dryer sheets; I'll try that this year.
Last winter and 3 winters ago I had tenants in the blower motor.