Monocoque bikes have issues when the base of the fuel tank has a hole, it can weaken the frame. DO NOT TRY TO JUST EPOXY IT. The bike may fold like a taco on you, likely while doing 50km/h...
Best suggestion is to poke really severely at the rust to determine how bad it is, it likely need welding a patch on it. Bet to do that anyhow, and get yourself a upper stress bar to brace the frame. Does not have to be a huge bar, just a goodly strong one. You will lose the helmet holder (that no one ever uses) when you add the bar between the seat post tube and the fork tube.