A big problem with older motorcycles is petcock problems.  They're a big reason for hard starting, stalling, no start, and leaks.  I took this one apart because it had "no reserve".

It's best to drain and remove the tank when working on the petcock.  The big nut spins on the petcock.

First thing to check (and you can do this without taking things apart) is the sediment bowl on the bottom of the petcock.  Water and particles from the tank SHOULD get caught in the bowl.  The hex on the bowls is famous for stripping, so use a good wrench to unscrew it.
A lot of folks poke holes in the little filter screen here, don't do it.  Note the tapered rubber ring between the bowl and the filter to make a good leakless seal.

Often the "tank filter" stays in the tank and gets forgotten about.  It has two screened windows which will get clogged or gummed up.  If you have no reserve, this is probably the problem - same with no flow or gas starvation.  It cleans off nice with carb cleaner.  DON'T just poke holes in it.  The bottom windows are the reserve inlet.

Here's the parts.  See the short tube on the petcock body?  Above that is normal gas, below it, it taps off the reserve section of the petcock.

Here's the vacuum operated part of the petcock.  Note that the spring is in the outer section and holds the diaphragm closed against the visible port in the petcock.  The vacuum line from the engine to the petcock causes a LOT of problems with hard starting and mysterious stalling.
Check your hose for cracks and if it's old or hard, replace it with HEAVY DUTY hose.

Some folks switch the spring from the outer section of the vacuum cutoff to the inner section.  This will hold the vacuum part of the switch open at all times.  Then they plug the vacuum tap in the head with a screw.  This means that the operator only has the mechanical part of the petcock to shut off the gas - so I can't recommend it.

Then put it all back together and go.

I've also seen a bunch of leaky petcocks, not from the sediment bowl gasket, but externally from the toggle. If it is leaking externally, it is probably leaking internally, too.  You USED to be able to replace the rubber biscuit that they use for the washer in there and refasten the metal frame with self-tapping screws.  The Ascot petcock has rivets there, and it may be possible to tighten the fit by resetting the rivets, or even drilling them out, buying a replacement rubber biscuit, and reassembling with self-tapping screws.  Ask your local independent shop, or check out some aftermarket places for the biscuit, I believe they are available.