Help ID'ing Omega Automatic

Hello,
I'd welcome help identifying the vintage and model of my grandfather's Omega watch. He lived from 1904-1982. I've searched through hundreds of photos of similar watches online, but have not been able to find this exact match. I suspect that it could be from the 1950s, when he was mayor of a city in upstate New York (1952-1954) . It's pretty scratched up, the face looks like it has some corrosion, and has not been serviced in decades, but the hands still operate when wound. Unfortunately, I don't know how to open the case to offer more photos.

On the back of the case, there is an engraving -- a star, followed by the words "14k GOLD FILLED."

My grandmother gave me the watch when I graduated high school in 1982, shortly after my grandfather died.

Thanks for any advice!

Thank you so much for the quick reply! I had found lots of similar-looking watches online, but none that also have the circle connecting all of the seconds increments. Would that be consistent with the caliber 351/354 bumper? Apologies for my ignorance about watches and unfamiliarity with the proper vocabulary. Very much appreciated.

Thank you for the advice!

Have you tried opening up the watch and looking at the movement and inside the case back? It would likely have all the info you're after. That's how I confirmed the identity of my Dad's old Seamaster.