The images showing the barrel indicate it has a good surface without excess oxidation or rust. If a signature is present, it should be visible. It would be located several inches behind the rear sight on the top barrel flat, usually as a first initial and last name, at times as two initials. Sometimes when written in old script, it's a little hard to figure out at first glance, so if anything is there, please post a couple images of it, taken with the light coming from different directions to highlight all details.
The gun appears to be in good condition with a nice patina, without any need for cleaning... but it looks like the butt plate has had some cleaning to removes patina/oxidation already.
Shelby Gallien