Newly installed freshwater pump with a hickup

[seatotaler]

Recently I posted a thread about having difficulty with my freshwater pump and accumulator system and it was suggested that I switch to the Shurflo Aqua King II that doesn't require an accumulator pump.
I installed it yesterday and it works great. However it has a hickup. Kickup being the operative word. About every 5 minutes or less the pump comes on but only for a micro split second. Much like a hickup. The other thing I noticed is that unless the tap is on full, the water flow surges and I can hear the pump switching on/off continuously. The water comes out of the tap but I can see a volume change in the flow. This will happen until the tap is at least 3/4 open. Then The pump stays on full and I get full flow volume of water. At one point during experimenting I noticed that if I didn't turn the taps off in the shower super tight the pump would come on and off at about one second intervals. That made me thing maybe the valves needed new washers and air was escaping, but not enough water to show a drip, since the show head is at the end of a SS flex hose, that hangs about 3 feet higher than the tap set. So I replaced those washers, but I still have the same results. I just replaced the galley tap set, a week ago. I'm going to check the tap set in the head and possibly replace it, but it doesn't drip. I believe that tap set is the washerless cartridge type. There are no leaks in the system. I've held a paper towel under all the connection and it remains dry. I installed the filter that comes with the pump in the proper place and the clear canister is screwed on tight.
Has anyone ever experienced this or have an idea of what's going on?
Cheers

[seatotaler]

I forgot to add that according to the instructions the pressure can be adjusted. On the end of the pump there is a tiny allen set screw. I'm assuming that is where Shurflo is saying that by adjusting that set screw the pump pressure will change. Perhaps it needs to be slightly turned, But I'm not sure if it should be screwed in to increase shut off pressure or screwed out to decrease shut off pressure. Or how far to turn that screw.
Perhaps that's not even the solution, I'm just speculating.