Sounds like at least one of those valves was the valve to switch the water pump to draw antifreeze during the winterization process. I have two valves that are utilized when winterizing my Wildcat. One valve bypasses the water heater and the other valve allows the water pump to draw antifreeze from a hose in the service area.
I have accidentally left the winterization valve for drawing antifreeze into the water pump in the wrong position in the spring and had the water pump sucking air like you describe. It was a head scratcher for a moment or two until I realized the valve was set incorrectly for the regular use of the water pump.
2014 Wildcat 312QBX
2014 Ford F350 SD 4X4 CC LB 6.7L PSD
Bob & Debbie, USAF Retired