I don't think it can be the check valve in the fuel pump... They don't have check valves...
IIRC those are regular old Carter cigar shaped pumps...
Your problem is in the Switch Valve I'm betting... Which is foreward of both tanks a tiny bit, and quite a handfull to change
Not hard, just a hassle...
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My fellow Americans, I have not been entirely truthful with you. I did gagoogity that girl. I gashmoigitied her gaflavity with my googis. And I am sorry.
