Any suggestions for care and feeding of a gecko?

…at least I think it’s a gecko. It’s only 4.5 cm long including a 1.5 cm long tail. Last week, I drove a car up from Ft. Lauderdale, Florida up to Western NY where we have snow something like 8 months out of the year. I came out the car this morning (temp 8C or 45F) and found what looked like a dead gecko on the driver’s door. I picked it up, put it on a tissue, and placed it in the sun on top of my wood pile. After about an hour it started to move slowly. I brought it in the house in a plastic container and it is moving much faster.
Clearly this is not a cold climate critter. I think he’ll make it if I keep him/her indoors.
What do I feed this guy? The google article says bugs, but that’s not going to happen. Sorry. I just made a soft boiled egg and will put some of that on a tray with water and lettuce.
I am open to suggestions: bacon? salmon? I can always put him back outside where he will become food for the birds in about 10 seconds but I want to give him a chance. He’s got 1700 frequent traveler miles on that tiny butt.
Should I just let him run loose in the house? Any suggestions?