First off, if the timing gear spray nozzle was left off, I expect that your cold idle oil pressure would be struggling to reach 40 psi.

I rebuilt my B20E about 10 years ago. The engine had around 140,000 miles on it. I did not fit a new pump; but, I did measure the end clearances on the pump (hard to do accurately) and they seemed to be OK. I did fit an IPD high pressure spring in the relief valve. On start up I had excellent oil pressure and continued to have good oil pressure until one day last summer. I was out driving around and all of a sudden the warning light on my after market oil pressure gauge came on at a stop sign. Revving the engine restored some pressure; but, the warning light / low pressure returned whenever the RPMs approached idle. My separate idiot light never came on.

I initially expected an electronic gauge problem; but, a test with a different gauge at the port showed exceedingly low pressure during cranking so it was a legitimate low oil pressure problem. Disconnecting the port and observing flow out the port during cranking showed very little oil flow so that pretty much confirmed an oil pump / seal problem of some kind.

Upon removal of the oil pump the seals on the interconnecting pipe were in place and showed no sign of damage. I pulled the pump apart to inspect it. The end plate did show slight signs of scuffing; but, as best as I could measure with feeler gauges the clearance was just at the upper limit of the service limits. It is possible that the oil pressure relief valve was sticking open (consistent with low idle pressure and sort of OK higher RPM pressure). Unfortunately, once you remove for inspection it is kind of hard to evaluate that. There was nothing obvious holding the ball off its seat.

I fitted a new Melling cast iron pump and seals from Rock Auto and everything returned to 'normal'. I have no obvious explanation for why my oil pressure went rapidly from OK to not OK.

Since you have a new pump installed I would definitely check for the presence of the oil spray nozzle. Removal of the timing cover may be a hassle; but, not nearly as much work as lifting the engine to get at the oil pump which would be the next logical step.

If you are up for it, you could do a relatively simple test by removing the oil filter and cranking the engine to check for oil flow. It will be messy (large catch pan under the side of the engine). If you have no flow or very little flow then you likely have a pump / seal problem of some kind. However, short of no flow it is kind of hard to judge whether low flow is too low. If you have what appears to be good flow then a missing nozzle is looking like a good candidate.