There is definately no extra battery for the clock. It´s driven by the regular 12V onboard battery of the bike.
I have been in there once, after my service tech at the shop messed up a warranty repair changing a defekt clock and left his lovely dirty black fingerprints onto the white tach/odo panel....not too difficult to get in, but still quiet a bit of tricky work that one doesn´t want to do very often.
I might want to go in there once again some day to correct also the tachometer needle to more accuracy. It´s showing off about 12km/h now.
Probably I will combine that with one of the next Brakefluid changes. We´ll see.