Unless he's an Astronomer his watch will be running on Solar Time and so it will be noon standard time and the sun will in the same place except for the equation of time correction.
If, however, the watch is running on Sidereal Time, which only Astronomers use, after six months he will be off 12 hours from the Sun. Sidereal wrist watches are occasionally found in magazines, but not often. Cheers, John Professor John P.G.Shepherd Physics Department University of Wisconsin-River Falls 410 S. 3rd. St. River Falls,WI 54022 Phone (715)-425-3196, eve. (715)-425-6203 Fax (715)-425-0652 44.88 degrees N, 92.71 degrees W.