If the watch is old enough it may require a mercury battery. Since the
mercury battery is of a different voltage than what currently replaces
it the watch will need calibrated. I own a 1965 Bulova Accutron that
was designed for a mercury battery. I found a jewler that could
replace the battery and adjust the watch for $20. Had some kind of
device that listened to the watch to determine how to adjust it.

I believe there are non-mercury 1.35V batteries, or 1.5V batteries with
dropping diodes.

The Accutron tuning fork vibrates faster at a higher voltage. (The user
manual warns that the watch will run slightly fast with a new battery, until
the voltage has stabilized. It takes a couple of days.) I don't know if the
adjustment has enough range to cover a 10% voltage increase.

I still have my father's Accutron. I ought to get it out and wear it. Very
stylishly retro.