Worked at a shop in the early 70's at the seashore. We repaired the ocassional rusty,leaking fuel tank. It can be done safely if you do things to keep an explosive atmosphere from being created inside the tank.
Necessary items for the job:
Copper sheet.
Soldering flux.
Shop vacuum and/or shop size air compressor. Vacuum must have an exhaust port for the hose.
Grinder. (Sander might work for surface prep)
Hammers. Body working hammers, but at least a ball pien.
Punch
Torch heated Soldering Iron. You do NOT want to be using a flame directly on the fuel tank. The original (vintage) method of soldering was to heat a hunk of metal (iron or copper) that would then hold enough heat to get your parts hot and melt the required solder. It's possible that there are electrically heated units capable of doing this job, but I would expect them to be commercial tools and very expensive! Anyway, you will have to hunt around to find this Iron, and will need a torch of some sort, like a plumbers torch, to heat the iron.
A roll of solder. Don't bother with the new non-lead versions, they don't work well.
Major rot may require tools to cut back to good metal. Don't leave rusty metal inside the tank, as rust particles will pass through most fuel filters and clog pumps, carb jets/passages and injectors. If your fuel system has an ongoing rust problem the only way to stop the rust from getting to the engine is a marine debris filter. This is a fuel filter that is basically a small deep tank that catches the rust by allowing it to settle out.
1) Remove the tank. Don't try this while it is mounted, as controlling the air inside it, and getting a good seal, is problematic.
2) Drain the tank, and then wash the inside and outside with a strong degreaser. You want to remove as much of the fuel from the pores of the metal as possible, and having a clean working surface on the outside makes a good seal easier.
3) BTW, it's possible that you won't find a pinhole leak using water, as gasoline will flow through smaller gaps. Using the punch, tap around the leak(s) to determine the extent of the bad metal. Using the fuel filler and pump/level sensor ports you may be able to see the area that needs work. You need to find the edges of good/bad metal to determine the size of the patch you will make.
4) Mark the area that will be covered, and clean it using solvents, and wire brushes, as needed to get solder to stick.
5) Cut a section of the copper sheet. The patch should be bigger than the damage, don't try to have the copper just meet the edge of a hole. You are making a patch, not a plug! You will be wicking the solder under the patch, not trying to "weld" the edge of the patch down. Think plumbing assembly, not welding/brazing.
6) You probably will have to form the patch to the tank shape. That's what the hammers are for. You may need to use some heat to shape the patch. Don't use a torch on it while it is near the tank. For some shaping you may have to solder part of it down, and then hammer the rest of it to fit. If you need to remove the patch for additional shaping, this can be done if only one section is soldered. If a lot of the edge is soldered, you probably won't have enough heat to flow all the solder to remove it unless you resort to peeling it up. That will entail starting from scratch, again. You can lay a second patch over part of the first one, if your patching needs to be extensive due to size or shape. Try to keep the solder thickness thin to get good flow and to avoid gaps. Remember that attaching another patch to an earlier one may flow some of the original solder, so watch for that, and make sure you don't leave a solder gap. Use the flux to prep the cleaned surfaces to ensure the solder sticks and flows.
While working on the tank, have the vacuum or air line blowing air into the tank. The sending unit must be removed so you get good airflow through the tank. DO NOT USE THE VACUUM ON SUCTION!!! It must BLOW air INTO the tank.
Try to position the tank so your patch will sit fairly level so the solder will not tend to run away from the parts. Thinner gaps helps to control this. Don't coat the repaired area with anything until you have confirmed it is leak free with the appropriate fuel.