I found a 4mm diameter little watch on ebay for USD4. It fits perfectly inside the one of the climate control turning knobs.
the process is quite straight forward: after disassembling the knob - which includes removing the panel from the dashboard and clipping off a few plastic clips, the top if the inner button can be sawn off using a thin meatl cutting blade. The clock fits perfectly as a replacement both in hight and in diameter.
THe only modification the clock needs is to make a hole on the removable back plate of the clock and a small hole on the display - so that the yellow light of the inner button can shine through.
it is enough to secure the clock to the bottom of the switch with electrical tape - it holds it strong enough to stop the clock turning with the outer ring.
Mod Edit: if can't see image, try this: https://imgur.com/WbDB6Mw
The only downside is that for resetting the clock or to change the battery, you need to disassemble again the switch. But that can be a regular summer maintenance job, I guess.