Do you have an end view of the tube or is it welded into the frame? My guess is the piece was welded with a resistance process because whoever manufactured the tube wasn't set up to weld tube as it's done today. The welding processes have come a long way since 1950. The problems you will encounter will probably be based on the tooling. The pipe being welded in Ulma Doctor's video is 6"-8" in diameter, but doing the same with a piece of 2.5" tube is a different matter. Tube and pipe are rolled in short sections in a slip roll or long sections with progressive rolls. When using the slip roll method the roll used must be heavy enough to form the flat sheet without deflecting. Taking an 8" strip and rolling it into a tubular shape is possible if you want a short section, but rolling a 24" long piece results with the ends coming together before the center does. I have a 3' roll with a 16 ga. capacity and the rolls are 3" in dia. and a 7' roll with a 14 ga. capacity and the rolls are 5" in dia.
The tube in your photo was probably rolled using a progressive method as shown in the video I posted but welded with the resistance method shown in Ulma Doctor's video. It's also possible the tube was formed over a mandrel to keep the shape uniform. Getting the esthetic look you want will be a dificult task because similar parameters exist for the resistance welder as they do for the rolling. Good luck in your search. -Russ