I know the OP talked about wet weather and water could be a problem BUT, it's also possible that there is no water in the fuel.
1. It could just be the ethanol/gasoline blend (AKA the norm for pump gas these days) is bad and gumming up the fuel system. While sitting for a month may not seem like a super long time, we're talking about a 33 year old truck.
2. Some of the fuel system problems mentioned by Ian and others, could very well be the problem.
Getting ALL of the old fuel out (if the truck runs, just burn that up by driving it) is a good first step. Filling the tank with good fuel and replacing the fuel filter is a very good second step.
The OP may need to pull the throttle body and inspect the manifold for signs of excessive fuel, but I would wait until I got new fuel and new fuel filter before I went to that step.
As for the potential of water in the fuel, I'm not totally discounting that. Just condensation alone in a partially empty tank can cause problems. However, I've never seen Seafoam, Heat, or any of the other additives that can correct large amounts of water in the system. They can help with a "little" bit of water but they are not the real fix. If fresh gas and a new fuel filter doesn't correct the problem, you're probably dealing with something more than just a little water in the bottom of the tank.
Ethanol blends are far more insidious than some folks realize, particularly in older equipment. One month of storage is plenty of time for problems to appear.
And I'm just going to toss this out there for general consideration - If you have a vehicle that sits parked for long periods of time; it is far better to keep the gas tank COMPLETELY full. This leaves no room for damp air above the fuel and subsequent condensation in the tank. The use of non-ethanol fuel and fuel stabilizer in those long term storage conditions will also help.