If your pump is located like mine, it is at the top of the water tank, gravity doesn't work unless tank is full.
I would look at the winterizing valve inards. Pry off the handle, remove the large nut, pull out the valve. Inspect the forks to see that all four are good, and the soft seal for any deformity.
If they look bad, they can be replaced without removing the valve body. Just purchase a stright line valve and switch.
Also check suction side connection of the pump head.
Dan & Sharon & Kasey (Our Yorkie Puppy (12 Yrs Old) On the Road (2012 Journey 36M, 2006 Jeep Liberty)
USN-Ret ('65-'93) Fulltimers, Class of 2012