I recently went through the same problem,  with the pump "blipping"
about every 4-5 seconds.  In my case it only happened when the gear was
down.

The problem was the dump valve.  In my installation it was very easy to
test by remove the dump valve and closing off the lines with some spare
fittings.  This cured the "blipping".  Lancair sells a valve rated at
higher pressure, but it is slightly larger and a lot heavier.  I chose
to replace mine with the same valve, figuring I can replace it again in
8 years if need be.

Bob Belshe
Moraga, CA
Lancair 235/320  494 hrs.