Got an old Time Timer off of eBay. Marked as "defective" - for 5€. Those bad boys usually are sold in the 35-50€ range (even 2nd hand).
Disassembly was rather swift, but those tiny cogs are quite a challenge.
Quick first look was a relief since all the mechanics were still working. The culprit was a broken wire from the coil to the PCB which could be quickly resoldered.
All the cogs back in place. \o/
This is a special little place in the Fediverse for a small group of purveyors of finest yak wool.