Does it start and run properly if you leave the fuel tank cap loose?
I doubt that it had two primers when it was new. That raises the possibility that one of the primers is causing a problem to the venting arrangement.
Having said all that, some of those things have a remarkable collection of pipes running in all directions doing incomprehensible things. Are you confident that the fuel system has not been modified by the previous tenant?
I'm wondering if the HT20 is a hedgeclipper model of the T20 brushcutter. Just in case it is, here is the T20 workshop manual:
http://golftechs.us/Manuals/shin%20trimmers.pdfI notice that the T20, and every other Shindaiwa brushcutter except one, has a duckbill fuel tank vent. I haven't heard that term before, but presumably it is the usual flattened tube vent that acts as a one-way valve, and is usually in the filler cap.