This entire case was just one big bluff, Cooper didn't need a watch since there was nothing he could do if they didn't keep his schedule...
There is another element operating in this hijacking that I see as crucial to how the Cooper hijacking went down: law enforcement was not in communication and failed to connect the dots in real time as things were happening, and they did not target their resources to where Cooper was at any given time ......... LE was operating blind!
The crew on the plane were not communicating with the pilots in the F106's, and that in turn was not being passed along to LE. Even if the F106 pilots had seen Cooper's chute open, that information was not being passed along to LE in real time! LE at all levels didn't have the faintest idea where Cooper was! He might as well have in China for all they knew. Reading 302's today 40+ years after the fact, makes that abundantly clear -
From a tactical point of view, apprehending Cooper was a complete fiasco. A system for keeping track of him minute-to-minute wasn't even in place! Himmelsbach and his helicopter might as well have taken off for the Moon, and it appears that is just about exactly what they did do!