Blainejr,
One thing you can do is hook up shop air to the pump. Put all the caps on tight, close ALL the valves and drains, and adapt one of the pressure gage fittings to shop air (you don't really need a lot of pressure - volume is more help - 50 lbs. would be fine) With the engine off, and a quiet environment, you can listen and feel for where the leaks are.
If the pump hasn't been apart, the leaks are probably:
1. dried out gaskets on the caps, suction & discharge.
2. Dried out packing
3. Leaks through the valve gates & handles.
BTW, don't run the pump for long without water in it - not good for it.
The air should not make it through the primer with the valve closed.
About the primer: The vacuum primer is really just 2 valves between the pump and the engine. When you pull the primer handle, you're opening the line from the engine intake manifold to the pump body. The primer has two float chambers - a primary and a back-up - that will shut off the vacuum when they fill with water. This prevents the rather terrible possibility of ingesting water into the cylinders of the engine.
It's an elegant solution - no electricity, and no oil needed. BUT, I would check it carefully to be sure it's working properly.
Let us know what you find - it's a process of elimination.
-Michael