Sounds to me like the float might be sticking once in a while. Try opening the drain on the bottom of the float bowl and catching whatever comes out in a can or glass so you can look at it. You might have some water or dirt in there. If you do, there might also be some in the fuel tank.

If you have rust in the tank, you are bound to have some of it getting into the float valve. Install an in-line fuel filter to block any more of it, and clean out the carburetor. I think there is a screen in the tank, but tiny particles will get past that. Carry a spare filter with you, in case the installed one plugs up.

Usually when people look for a leak in the intake system they spray WD-40 around it. When that gets in the intake it will make the engine run faster, I am told. If you actually find a leak, examine it to see whether it is actual damage, or just a place where maybe you didn't get it sealed correctly when you last cleaned the carb. You could probably plug a leak with RTV. Worth a try. At least if it doesn't work you can get it back off with no permanent damage.

You probably already know this, but if you don't, here goes. Motorcycle fuel tanks usually have an ON and a RESERVE setup. ON uses a little standpipe a couple of inches long to take fuel from some distance above the bottom of the tank. When the fuel drops below the standpipe, the engine quits. You then switch to RESERVE, which takes fuel from the bottom of the tank. The bottom is where the dirt and water will have settled. So when you switch to RESERVE you might suddenly have problems that weren't there before.

Edited to add: The old Alaskan bush pilots used to have to fuel their planes from rusty fuel barrels. They filtered the fuel through a chamois. It stopped rust particles, and also was said to stop water. I have never tried it, but you don't have much to lose.

You said you have rust in the tank. I imagine that means there was water in there, too. If you haven't already tried cleaning out the tank, this might be an excellent time to do so. Take it off the bike. Pour the fuel into some suitable container (through a paper coffee filter in a funnel). Remove the petcock. Hose out the tank. Put a cork in the petcock hole. Pour in a couple quarts of soapy water and drop in a handful of good-sized hex nuts (count them) or a foot of chain. Shake the whole thing around, including inverted (hold your hand over the filler). The hardware helps knock loose any rust or dirt. Dump everything out, and inspect the tank as best you can. Repeat until it looks clean. Rinse with clean water and use a hair dryer to blow out any remaining moisture. While it dries clean out the petcock. Reassemble. If your fuel seems OK, reuse it. Wouldn't hurt to pour it through the coffee filter again. With any luck, that ought to solve some problems for you.