I had the same water pump cycling issue a few years back. In my case it was the strainer just before the pump that was letting in the slightest amount of air. I always have to make sure that the strainer is threaded on very carefully and very tight.
2008 2500hd Silverado Duramax
2011 Northern Lite 8.5 lite
2006 Wildcat 27bhwb fifth wheel
2009 Lance 830 (sold)