The piece in question is a (now working!) Smiss made Wittnauer wrist watch, which was presented to Eric Broadley by Ford in 1963 when Ford procured Eric's services - as well as, of course, the rights to the Lola MK6 GT.
As is well known, it was the Lola MK6 that formed the backbone of the Ford GT project that was to be developed in the four times Le Mans-winning GT40 MK1 and MKII, and the Ford MK IV. The watch, which was recently sold by Eric's son Andrew, is in very good condition. Its face is inscribed with Eric's name in black, while the rear is engraved with the words:
I was told that similar watches were presented to the other individuals leading the Ford GT project, ie Carroll Shelby, John Wyer, Ray Geddes, Len Bailey, Ron Martin, Chuck Mountain and Roy Lunn, but I do not know if any of these watches survive. Has anybody out there seen another one?
C. Bradley Jacobs (www.watchcarefully.com has been able to fill in a little more of the history of the Ford-presented watches: "I chanced to come across your post about the Wittnauer watch formerly belonging to the Broadley family. In response to the request for information about additional pieces of this type, I refer you to a Bonham's auction of 2008 in which Mr Graham Hill's watch was sold:
Lot #155 Graham Hill's Wittnauer watch presented by Ford Total Performance, 1963, in 14 Karat gold, silvered dial with GRAHAM HILL to centre, FORD DIVISION TOTAL PERFORMANCE TEAM 1963 engraved to rear, 3cm diameter.
Sold for £920 inclusive of Buyer's Premium. (Details of the auction can be found Here - item 155)
I have no information about the others in this series--I expect Mr Shelby's watch would fetch quite a sum. One wonders whether he still owns or wears it."