Thanks to everyone for the replies. Here's the deal. Based on your suggestions, with the tank level indicating 1/3 full, and the pump in an unprimed state, I opened the drain valve on the tank and it dribbled out. I didn't catch it in a bucket and measure it because it was such a meager amount that it was apparent that the tank was essentially empty. It stopped dribbling out after about 20 minutes, leaving no appreciable amount of water on the ground. Bad level indicator.
I guess my problem changed from a bad pump to a bad water tank level indicator, which is a bummer because I always found the freshwater indicator much more useful than the greywater and blackwater indicators.
