It's not really a pressure problem. When you're just running out of gas on "ON" the pressure is just about zero. Switching to reserve gives actually you a higher pressure (until you run it dry).
The "ON" fuel pickup is about 2 inches above the petcock, through a simple brass tube sticking up. Junk, dirt, rust flakes, sludge, whatever... is at the bottom of the tank and doesn't get into the "ON" pickup tube easily.
The "RESERVE" pickup is a hole in the top of the petcock itself, actually down inside the petcock nipple on the tank (if you have that type) and it naturally fills up with all the garbage in the tank.
SO if the reserve fuel flow is way low, it's probably plugged with guinge so removing and cleaning the petcock is required. If you're down to reserve, you can probably lay the bike as far over opposite the petcock - lay the seat on a chair or something - and remove the petcock with little or no gas spillage. If you have the screwed-on-from-inside petcock you have to remove and drain the tank to get it off.
There's a plastic filter screen "sock" over the pickups, it gets clogged with goop too and if it's clogged below the ON pickup level then the reserve flow will be rather poor too. You CAN do without the screen if it's ruined but if you can clean and salvage it that's best.
You should fit a simple inline fuel filter between the petcock and carbs. This will eliminate a lot of "dripping carb" problems.
Draining and washing the tank out is a good idea anyway.
Oh, and a tip if you DO run dry: There's no crossover tube on the SOHC4 tanks I've seen, so when you run dry and coast to a stop the bottom of the tank is empty on the petcock side, but there's still quite a bit of gas on the opposite side. Lean the bike way over towards the petcock and that gas is available to get you at least closer to the next gas station!
If your petcock is assembled with screws you can take it apart and clean it, use some silicon petcock grease or electrical dielectric grease on the moving parts. If it's riveted you CAN drill out the rivets and drill/tap for small screws. First thing I would do is jusy blow with compressed air back through the petcock from the carb port, in ON and RESERVE. This should clean out the inner workings, probably the biggest problem is a buildup of goop on the top of the petcock. Just use a toothbrush and solvent to get it off, and get any sludge out of the reserve port with a Q-tip wooden stick. The sock is pretty easy to tear when cleaning, stick a pencil or marker inside and brush against it gently with a toothbrush.
