UPDATE: I know it's been a while, but I wanted to give an update to what I've done so far (which isn't much), what I'm seeing, and how I plan to proceed. I also had an oiling question.
So as Nucejoe recommended, I started by running the movement and seeing how long it took for the power reserve to run it's course which was actually just over 48 hours. That's absolutely within spec, so that ended up not being an issue. The second hand was still stopping at 3 seconds after 12. Unfortunately I had a rookie moment, and neglected to pull the crown out to the setting position (3rd) when removing the movement to run the next test. So without pulling the crown all the way out, it's impossible to properly reinsert it! So with that, I was forced to remove the hands, dial, date mechanism, and half the keyless works in order to get the stem back in. In that process, I found out that the stem is bent. I purchased this used, and when I received it the crown barely had the threads to screw down. Thinking a bent stem was related to that and not wanting that to happen again, I purchased a new Omega stem.
After that I was able to run another test and this time the second hand did not stop in the same place it usually did. Huzzah! I ran that test three more times and the second stopped at a different place every time! Success....except, because I had to skip a few tests (e.g. with dial on, dial off, date off and so forth) I don't know EXACTLY what that issue is, but I at least have an idea.
Next up, the balance. On my inspection, I could not find any obvious faults. The cap stones did not look out of place, unless its very very slight. Wasn't sure how visible a shifted cap stone would look. I have observed that it does not stop its motion in what I would consider a natural way. It stops rather suddenly. I did purchase (in all my many purchases for this project) an etachron key, as well as learned what its for and how to use it. I carefully opened up the regulator pins on the etachron system and removed the stud (I learned this from another video) and removed the balance complete. My initial inspection at 15x did not show any obvious bends or anything like that in the pivots. So I just ordered a USB microscope and will take a closer look. Hopefully the pivots just need to be thoroughly cleaned, but if not, I already have a balance complete I can use (I don't have the skills nor tools to replace a balance staff). I'm hoping it won't come to that.
Once I removed the balance, and the pallet fork, I ran the gear train to see how that looked. Again, what I'm seeing is that it doesn't release power in a smooth natural way. It gets choppy at the end of the run where it will stop-go-stop-go and then finally stop. If you shake it a little bit it will go just a little bit more. When I received this watch a few years ago, I was told it was serviced and was given a service record, but on my inspection, the parts are not nearly as clean as I would like them. I have found residue on the bridges and rotor, and the gears do not look as clean as I would hope. So I don't know exactly what was done, but I'm not confident that all my pivots are as clean as they need to be. Or that it was properly oiled.
So that's it...that's where I'm at right now. I plan to disassemble bit by bit, and inspect everything (endshake, sideshake and close microscope inspection) so I can hopefully fault find. I'm sorry this was so long, thank you for reading if you got all the way through. One question I did have concerns oiling. I've watched Marc's video on servicing the Omega 2500 (which from what I understand is exactly like the 1120, but with the co-axil) and I've noticed that he oils the winding pinion, sliding pinion, and stem with Moebius 9501 (cause it's blue) and not the recommended HP-1300 (which is red) from the technical sheets. I do not have the 9501, I purchased 9504 instead cause that was a change that was made on the technical sheets. So which should I use? Is there a reason that the HP-1300 is not used?
Ok, again thank you so much for your input. I didn't add pics, cause I didn't think there was anything to really show just yet. It looks like what you'd expect.