This effectively amounted to replacing a battery but I still learned some things along the way.

It was thankfully easy to take the rubber case off which I expected to be glued or something but I just had to pull it off.

This revealed the main board with the LEDs and the battery tucked underneath.

base of light with cover removed

It turned out to be a 18650 lithium battery.

base disassembled showing the battery connected

Adam Savage has since released a video about 18650 batteries which probably explains why it stopped working.

You’ll get a lot of options when searching for 18650 batteries but the tricky part was finding one with the right connector.

jst connector of the battery

This replacement worked