Gruen Veri-Thin 'tank' watch

Factual Questions
1

I have a Gruen Veri-Thin ‘tank’ watch similar (but not identical) to this one. The crystal has a pronounced angle horizontally across the middle, the second hand dial (?) is circular and without the box around it, and it doesn’t have the ‘bolsters’ on the crown side or other side. (NB: The crown is missing.)

Question 1: Can anyone tell me anything about it?

It is engraved on the back with my grandfathers name, and below that some numbers in the format XXX XX XX.

Question 2: What are the numbers? They are in the wrong format for a Social Security number. To my knowledge my grandfather did not serve in the military, so I don’t think it’s a serial number. It’s not a date.

2

WAG, is it a watch serial number? The watch you linked to also has a seven digit number on the back.

3

The number is under the name, and it looks like the same font. It also has spaces.