Well, I have successfully disassembled and reassembled an Elgin 554 15J. This is the first time for me on any watch! So, I feel good having accomplished this much so far. However, the watch did not run before and it still doesn't!
So, now as a neophyte, I have a few questions for you seniors.
I was unable to wind the watch. So, I took the mainspring back out, (Actually, I've disassembled the whole watch again) and examined the mainspring in the barrel, which I didn't do before. The mainspring is not broken, so after reassembling, the spring will not "catch" in order to wind it. This spring has a hole in the center which appears to be intact, but the barrel arbor seems to be worn. It has a barely noticeable notch on the side of it. I've never seen one closeup so I'm not sure about that.
Also, I noticed that when I did have it back together, the stem turned the canon pinion in both the winding and setting positions. Haven't quite figured that out either.
If I resolve these problems I think this old watch might run. Oh, I did notice too that the center wheel has quite a bit of side to side play in the bushing, (not jeweled).

Any thoughts or advice will be greatly appreciated. As you can see I need a lot of it.
Thanks,
Dave