I don't drive a Tesla, and clearly don't have their insurance, but have had my rates affected by driving between 12a and 4a.

My insurer (not a cut-rate one) did give me a discount for using, for 90 days, one of their OBDII dongles. That dongle measured a few things, one of which was number of times I drove between 12am and 4am. (Others included number of times I hard braked, but none of them was how fast I was actually going.) I'm a night owl, so the 12am part was frustrating.

At least for this particular insurer, the discount sticks after you send the dongle back.