An ordinary Casio or Timex is sufficient. Here is the trick. DO NOT reset your watch! Instead, check it once a week against the time ticks from WWV or WWVH. Slightly more dependable than setting by
internet time and more accurate due to update interval and timing of the
screen update than setting by your GPS unit. Back to the watch... check it weekly and
record the correction to correct time. While actually at sea, try to get a time check daily. Then after a month, start calculating your
rate. That is how fast it gains or loses. If the rate is consistent then from your chronometer log you can always apply a correction to watch time to get GMT.
Joshua Slocum, on at least one occasion, checked his
cheap alarm clock that he used for a chronometer, using the Lunar Distance method, which will seldom be better than 10 seconds of accuracy. And he made the first
circumnavigation by a solo sailor. A standard digital wristwatch will be plenty more accurate than that, once you know your last correction and the rate.
You can do what professional navigators are taught to do, and use a hack watch and subtract elapsed time from chronometer time, or do what many or most professional and accomplished amateur navigators ACTUALLY do. Bring down your body to the horizon and then take your time looking to your watch. Count "thousand-one, thousand-two..." etc and have your eyes focusted on the watch at the five second mark.
Record your time, then look at your
sextant for the Hs. You will be within a half second, good enough by far for
small boat navigation where the accuracy of the observation is usually your limiting factor due to platform instability and raggedy horizon from being down in the waves instead of 70 or 80 feet above them like on a ship.. A one mile triangle for your fix on a small yacht is pretty excellent. Sometimes you will struggle to get it tighter than 4 miles. A half second on the time is more accuracy than you can make full use of.
Also, always complete bringing the body down to the horizon as you are on the top of a wave.
There are a few other tricks you will learn if you study and practice for very many years.
Before you bother
buying a dedicated timepiece for
navigation, or a
sextant and tables and almanac, practice making plot
sheets and keeping an accurate DR track. This is the most elemental form of Navigation and serves as a basis for picking your Assumed Position which you need to calculate your azimuth and intercept, which you use to draw your Line of Position, two or more of these, usually three, that you will advance or retard to an arbitrary time, (typically noon, LMT) for your daily fix. Your DR is of extreme importance and you can even make a sometimes surprisingly accurate landfall using only your DR. And you don't need any
equipment except paper, pencil, dividers, and triangles.