Thanks, everyone, for your suggestions.
Doc Bob: I must admit to being a bit of a novice when it comes to identifying a squeak's source. I have checked the vacuum line to the vacuum advance, and it seems to be solid, and the plug in the manifold is still in there tightly.
Crenwelge: The fuel pump was "new" last summer; It's one of the more modern ones with the all-metal housing. It's entirely possible that it had been in the warehouse at my FLAPS for a while, though.
The Tank was redone last summer as well; I had the local "Gas Tank RENU" place do it, and so far, so good. If there is debris or something in the tank that is big enough to block the petcock, then it came in the gasoline -- which is a possibility. That will be the last thing I check I think... There's about a half-tank of gas in there, and I don't have a 10 gallon pan to drain it all into.
Jerry: I will try the wiggle. There is gas at the pump, but I didn't remove the line from the pump, I just loosened it up so that it started weeping. I will pull the line going up to the filter and carb and check to see how far the pump will shoot the gas.
I haven't tried a gravity feed tank. I may be able to get my hands on a motorcycle tank, or perhaps one off of a small garden tractor... or, if push comes to shove, fab one out of a gas can. What do you recommend?
