You may have hit on the solution.
It appears it may be an obstructed vent. There is no easy way to disconnect this to see if it is clear. I filled the tank as full as possible holding the hose in the fill tube to try and get the water to come out of the vent. It would barely come out. I used a needle to poke through the holes on the metal screen to open it up.
I turned the pump back on and opened a faucet and it quickly primed. When I opened and closed the faucet the pump would turn on and off as expected. I then proceeded to open all the other valves one at a time and the air quickly escaped and I had good water flow.
So far so good. I will just have to see if everything continues to function when the tank gets lower.
Thank you for the recommendation. I also thank everyone else for their suggestions.