posted 06-17-2020 06:31 PM
For a detailed description of the satellite clock, see the Mercury Familiarization Manual, chapter 12-22 (page 367).
While the time of day clock is hand wound, it is apparently not possible for the astronaut to adjust the time.
However, the Flight Operations manual has a step in the countdown checklist at T-90 minutes for the satellite clock, where the astronaut is supposed to wind the clock knob, and check that the displayed time is correct with ground control.
So it was probably set by a technician before the flight.
I have no knowledge of how long the clock could run without rewinding, but as a reference, the Earth Path Indicator was supposed to run at least 20 hours without rewinding.
One can assume that the clock would run longer than that, and maybe even longer than any mission possible with the Mercury capsule (a couple of days).
The MA-6 Flight Operations Manual is here: Checklist item about the clock is point 41b on page 13.