NavList:

I have a Casio atomic.  After repeated checks against various sources, i find it is exactly 1 second fast after being synchronized.  My easiest accurate time appears to be the UTC output of my GPS on the boat.  After it boots up, and you wait a time quoted to me as 14 minutes, it supposedly has downloaded all new data and re-synchronized.

I manually adjust for DUT 1 off the naval bulletin.  DUT currently adds +.3 seconds to get to UT1.

The watch has been perfectly consistant as +1, so it is easy to use a known correction. My GPS and watch track UTC exactly one second apart.

I do sights by starting a 360 degree dial stopwatch precisely off my time reference, then hold it on a lanyard wrapped in my left hand. That way when I get that precise pass shot for a fraction of an instant I just press the stop with my weak fingers, as the strong side fingers are in position to turn the drum. I then just add the stopwatch time to my start clock reference.  As I use my sextant without glasses over my eye, I can't glance at the watch without a lens on, I need reading glasses. 

I actually have a pair of reader sunglasses with the right lens out, so I can instantly glance at a watch with my left eye in bright sun and read it.

The dial stopwatch I use is actually pretty old, and was my fathers for the same purpose.