Fiberglass
 

I have done a lot of body work on cars, not so much on garden tractors, but metal is metal and should not be much different. If it were just small pin holes, I would have the panel sand blasted, apply masking tape to the outer surface to provide a backer then apply fiberglass (liquid resin with hardner) to the back side and if you worry about the metal being weak, embed some fiberglass cloth into the resin, this will make it as nearly as strong as was prior to rusting. Remove the tape (may have to hit it with flapper disk, fiberglass will stick to the tape too) and apply a very light coat of body filler (bondo) to the outer surface and sand it smooth. I would not worry at all about vibrations loosening this repair...by having it sandblasted prior to repairing it, it roughs up the surface to allow the fiberglass/ filler bond to the metal, as well as eliminating all the rust.

Thanks Westofb for the great information. Repairs on this side panel are done and can be seen in the pulling section under "Project: Nemesis".