It appears that a PO had jury rigged the air valve (prob'ly 'cuz he didn't want to pay$30 for a new one), 'cuz if you look at part # 1203W in the exploded drawing on page 9 in PHII owners manual
PH II Owner’s Manual you'll see that there is no black piece TO break off...the air valve is complete in the white nut. I think you'll find this bit of info from Raritan useful:
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PH II Air Valve problem/cure
The air valve is part #1203W...the little square plug on the front of the pump. It has has a check valve inside that opens on the downstroke of the piston to allow a little air to come into the (unused) top half of the pump cylinder to stop the "vacuum kick." If this check valve doesn't open to allow air into the top half of the pump cylinder, the handle becomes very difficult to pump in the dry mode and wants to jump back and smack you in the face. This ONLY happens in the "dry" mode. When it happens it means that little check valve is stuck.
The cure: Straighten a paper clip and poke the wire into the hole in that little plug to push it loose...it's spring-loaded and you should feel it move in and out when you press the wire in there. If that doesn't fix it, remove the square plug (it threads into the pump) and clean it. Wrap some teflon tape around the threads to seal it when you put it back. If THAT doesn't fix it, replace the air valve.
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Which is prob'ly what you'll have to do, thanks to the misguided efforts of the PO 'cuz what both of you have done is no longer an air valve or any other kind of valve, it's just a plug. The good news is, air valves typically have about a 10 year lifespan.
--Peggie
"If you can't explain it to a six year old, you don't completely understand it yourself." --Albert Einstein