Mike's priming method is correct. At times when I was chasing a similar
problem, I found that the diesel pickup pump base and pickup tube were warped
at the pump base (junkyard engine source). This led to a loss of prime and an
intermittent inability to reprime often for 30 seconds or more. I had to true
the two surfaces (base of pump body and top of pickup tube) by emery cloth
sanding against a flat.

On my oil cooler/filter mount, there was/is a predrilled port for mounting
another oil pressure sender or temperature sender. I have been known to take
that out, add a tube and prime. This is my approach after I have pulled the
pan for some reason.

Frank Grunthaner