I know I am late to the party, but I was led here by a search also trying to find more about this gun after watching an episode.
I have the gun picture paused on the screen right now.
It definite has a very large S engraved in it, with a G in the center of the S. The G is about 1/2 the size of the S, with the S passing through the center of the G. This S is centered on the screw behing the cylander, around 1/2" back from the screw.
The gun is blued. The S and G are gold in-layed and there is 2 gold in-layed rings around the rear of the cylinder (1 in front and 1 behind the index notches).
The view I have on the screen it looks like a cartage pistol. but when you search on dead mans gun on google graphics it brings up pictures of the DVD case for the show, which differently is a different gun.
My vote goes for the SG is George Schofield.