Over the years, that has happened to a few of mine...
I put a little denatured alcohol in a fuel bulb and carefully push it into the pump. Once you un-stick the inlet check valve, a little of it will flow in and if you let it set for a while, it will soften the gummy old fuel, and you can work more in there until it finally starts to come out the other nipple. Then I put a short loop of fuel line on that connects the inlet and outlet nipples, and with some alcohol in there, I flip the prop a bunch of times looking for movement of the liquid in the line. Then a good flushing of whatever gunk is in there, and it's ready to test run.

Out of about a dozen, the only Perry pumps that I've had trouble with (2 of them ) are backplate pumps that have sat un-used for 20+ years...(one pumps bubbles, and the other drips fuel out of the weep hole )