Cause he's an archeologist, get it? ...unearth... ha. He he. Anyways, this came up on my Facebook feed a few days ago, and for once, is something interesting enough to share. Indy uses a Gillette single ring traveler set. Edit: As far as I know it's not common knowledge.
More importantly is it an old type or new and improved since both styles were sold in that style traveler case.
The movie is set in 1938. Indiana jones was 39. Assuming the razor set was purchased when he was 21, that would make the razor set new in 1920, though it could be from any time between 1915-1938. What I don't really see in the picture is chrome blade cases, which kinda makes me inclined to believe that it might be a Gillette Bulldog traveller. ...or an old type. The set dresser is probably the only person who knows for sure.
If it is sort of period correct, it could possibly a Gillette Cruiser set which was produced no earlier than 1930. It had a New short comb razor in the set. Only thing that may rule it out is if they never made any of these in a nickel and/or silver plating.
I have this set... of movies in 4K. I might rewatch them soon, and see if I can't capture a sharper image of the razor.