Did you measure to see if the key switch is shorted inside?
If you got away without blowing the fuse there must be thermal cutouts in the lock motors, or maybe you put a penny in the fusebox.

If you decide to cut and repair with shrink tube and non-insulated butt connectors
be careful and buy only made in USA copper butt connectors.
Recently I had an adventure on ebay with a kit of 300 (3 sizes) shipped
from the USA. They were:
1. NOT copper
2. the wrong sizes for who knows what size wire
3. They had seams.
The vendor later claimed they were brass and looked like aluminum.
I tried to return as they were not as advertised, and the seller refused to send a shipping label, saying he'd return the postage and credit together. NOPE!
I beefed to Ebay and it turned out that it was a Chinese merchant and he expected me to ship his rubbish back to China. Yikes!
Postage to China costs an arm and a leg, there's no tracking and he would have claimed that he never received them. This happened several years ago with some LED headlights, maybe the same rude dude?

The good news is that Ebay decided that I got a refund and can keep the junk.
I reordered at slightly more from a place in Texas, and got the real McCoy.

You can replace that crummy combo trunk light and 10-watt heater
with an LED panel and have super light in back.
Here's one option with 5 panels and socket adapters including the trunk festoon lamp/heater.
Don't ever grab a hot trunk light, it's bad for your buttermilky fingers.

https://www.ebay.com/itm/283975046870

Good luck with fixing that, no way you gotta cough up 275 clams, Bill