PV panel ratings are a little weird. The typical 12v panel probably shows 22v no load, and 1amp at a dead short. At 12v you get something in between, but not the 0.8 amps that a “10 watt” panel would be expected to provide. now, the tech has improved a lot and my numbers may be dated... but I get about 1 amp into 12V with a 50w panel on my camper shell. So: I don’t think the 10w panel, further derated if run inside, is going to push much current.
if youre committed, a flexible panel, glued to the trunk lid, would provide more reasonable trickle power, enough to use a real charge controller.
with my camper shell, this was fine... I was drilling holes in fiberglass. In a sedan... it would depend on how long I’m keeping the car. A wagon, however, could have a panel laid down on the long roof with the leads run under the rear lid weatherstripping, or perhaps down the windshield under plastic trim, into the hood. check for flexible panels on Amazon.