Well I searched through pages and pages of vintage watches of every make suggested on this and the other thread, and only one watch came close.
At this point, I'm pretty sure it's the 50s era black dial 'Westclox Wrist Ben':
. . . which would be consistent with the kind of watch his teenage character would wear.
It's cool to note that most the other wristwatches Dean wore in real life had black dials, so he might have had something to do with the choice.
Thanks Watchbreath for the lead.