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Hello Joe,  I made one mistake in my earlier posting.  The Tag Heur watch that Beebe used was not a stop watch but a high grade seconds setting watch.  Since Beebe would have been familiar with all of the GCT watches availabe (Hamilton, Watham, Longines, etc),  I suspect his choice of the Tag Heur was that it had a mounting bracket made for screwing into the dashboards of sports/rally cars.  I think you'll find that a little work with a sheet of plastic, a coping saw, and a bit of heat (ovens work,but wear thick gloves!) you'd be able to make a secure bracket that still allows the watch to be removed.  As to how accurate your time must be, I have a copy of an early 40s article by PVH Weems on rating watches (by which he means high grade railtroad watches) where he indicates that a couple of seconds error is not of much importance in the entire sight tatking/ sight computation/ plotting process.  No one need agree!

Cheers, John