A bit more than 12V

That wall-wart is a piece of crap. It claims to spit out 12V DC, capable of 500mA. I used my dummy-load to test it a bit. I had to pull close to 700mA out of it to make its output drop to 12V. It will go into the recycling bin right away.

Fortuitously I found a switch-mode power supply that goes up to 15V. I'll use that one instead. As the wallwart only consisted of a transformer, rectifier diodes and a cap, all the battery charging logic must be in the car-jump-start device itself. Shouldn't be an issue.