12V solar battery charger for $10

It wont help anything unless you let the car sit undriven for weeks or more without driving much.

and in many of today's vehicles the cigarette lighter connection is disconnected when the ignition switch is off....

A constant current flow through any lead-acid battery shortens it's life. Every time you deep cycle and charge or jump start it, you take a little of it's life and take a chance on damaging it. They do make a battery maintainer, in both electric and solar, that shuts off completely when a battery is full charged but should only be needed on a vehicle battery if it's not going to be driven for extended periods. HTH, Dave