Pretty common problem and agree with above posts with few exceptions. It won't be your vent line because a pinched line inhibits the replenishment of air in the tank as the fuel is used. Switching from "on" to "res" would do nothing to illeviate that problem. Your bike is 18 years old. Any original rubber on these bikes is due for replacement. All vacuum lines, belts, and seals in carbs are prone to failure. Petcock is a given after all the years and gallons of fuel delivered through it. Another overlooked item is the fuel strainer that sits over the petcock stem. Often times it does not come out with the petcock and is therefore not seen. The strainer in your bike, if original, is deformed and possibly clogged in such a way as to restrict full flow of fuel when the petcock is switched to the "On" position. Switching it to "Res" opens a port lower on the stem and thus a new entry for fuel to flow through. I would recommend buying the "cover kit" mentioned above and rebuilding the petcock, as well as removing, cleaning and possibly replacing the fuel strainer that sits on the petcock.
