Omega Seamaster/Railmaster PAF Advice

Hello all,

Starting my time off here with a big request, I guess. I hope I'm not running afoul of any rules or norms. These things happen when you join a new forum with it's own standards, but I did my best to read a lot first.

In my personal search for a Railmaster to transition from my grandfather's railroad grade pocket watch collection to my own wrist watch collection, I came across a number of PAF pieces and references to them online. I tried to do as much research as I could, but it seems there's a number of variations in dials and casebacks and some resources, like Hodinkee's article from almost a decade ago, aren't available anymore.

I came across a Seamaster PAF from an online private seller. He has a letter from the auction he bought it at and an extract from the archives but it seems like if anything its a less common case back that I'm not used to. The condition is not the best, but I want to see if it seems legitimate before I start seriously considering.

Pictures below. Thanks ahead of the help.

Perfect answer, thank you gemini4. In looking at all the things like dials and case and condition, I made the stupid mistake of neglecting thinking about the movement not being the 135.004. Maybe in part because I didn't see the movement until today after looking at this for a week. Case closed, no pun intended. Thanks!