Not Seiko, but the next best thing:
Omega Speedmaster cal 861 "Moon Watch" - first watch on the moon.
References to the implementation of the chronometers can be found during EVA preparations, i.e after the Eagle Lunar Module has landed.
The first reference comes on page Sur-27 of the Surface Checklist (at 106h49), where the begin donning the PLSSs (Portable Life Support System or backpack) and the Oxygen Purge Systems (OPSs). Chronometers are fitted to the RH gloves, which at this stage are not donned:
Page SUR-37 mentions the chronometer on the RH gloves:
The gloves themselves are donned at 108h42:
Prior to the EVA, hacking of the chronometers takes place:
And a little later:
And the rest, as they say, is history...