I bought a 05 350z At a good price and I really like the car. But I have noticed at a stoplight while the car is idling the oil pressure is very low. When you take off and give it gas the pressure goes up. Is it normal for the all pressure to go very low while idling. It registers only slightly above zero while idling

It may or may not be normal. The pressure can drop to as low as 7 pounds using a good mechanical gauge but as long as it comes up at off idle to 20-30 pounds you are probably alright. The old rule used to be 10 psi needed for every thousand rpm.

Unless you're verifying with an external gauge, the factory gauge can't really be trusted. Nissan has a habit of making the sending unit sensor hole extremely small, which lets small debris get in there and block flow.

Randy, does your 350Z the RevUp version of the VQ (Track or 25th Anniversary trim/model)?

How many miles?

It’s not then trck version ! It’s has the DE engine base model with 130000 miles . When you start it cold the pressure is good until it warms up . Once the car warms up the pressure get very low when you at a stop light it does go up when you take off but goes Low again when you stop again .Also the oil light comes when stopped but goes out when you give it gas

'Unless you're verifying with an external gauge...'

This. You back up check with a known good gauge. ALL engines give decent pressure when cold, it's hot that matters.

Checking pressure with an external gauge is a good place to start. I'm enough of a car hypochondriac that I'd probably just jump right to a compression test.

Yep - check it with a good gauge but more than likely you have a nice set of worn out bearings that are leaking oil like sieves. It happens. If the good gauge reports the same thing, move up to a thicker oil.

First of all check that you have the proper oil level in the car. It helps if you know you have a) healthy oil and b) a proper/good filter installed. More oil or less oil will cause a fluctuation in pressure and for this you want to be accurate. Check pressure with your own gauge. (autozone has loaners). If pressure is good at idle (approx 14 psi) then replace the oem sending unit.If pressure is below normal (under 10psi) then most likely the oil gallery gaskets are worn out. Known VQ engine issue.