Check it with a mechanical gauge to ensure pressure is OK as others have mentioned. If pressure OK, replace the OP sending unit. Try and get an OEM Nissan part. Beware of cheap off shore brands.
I worked for as a Nissan Parts dealer in the 70's through 90's and the oil pressure sensors often failed. Never sold a single OP gauge unit in 20 years for a Z ( or any other model ), but lots of oil pressure sending units. They usually failed with a low or Zero pressure reading at idle. Sometimes they were erratic. All signs of a failing OP sending unit.
BTW, a healthy engine should show a minimum of 10 to 15 psi. Oil pressure at 800 rpm with 10w-30 oil at operating temperature. If you're below 10 psi at 800rpm your engine is probably getting pretty tired, and bearing clearances have probably opened up ( worn bearings ) . Original poster has a newly rebuilt engine, so if clearness are correct, oil pressure should not be an issue.
Golden rule is 10 psi per 1,000 rpm ( Hot ). Always check with an accurate Mechanical guage. The factory electrical OP gauge and sending unit are NOT highly accurate.
Edit: OP lives in Nevada. Extreme ambient temps there. I would suggest using a good 20w-50 for that climate. These are an older design engine, with larger bearings clearances than you see specified on modern cars. Beware of running too thin of oil.
Personally, I run a 10w-40wt Joe Gibbs synthetic in the PNW ( BC ). This is on a brand new engine. We can some pretty high ambient temps in BC... but nothing compared to Nevada. I don't run the car in winter.
Edited by Chickenman, 01 October 2016 - 11:42 AM.