The same thing happened with me when I first bought my Z. I thought I was in serious trouble, but it turns out the inlet to the oil pressure sending unit is very small and can become clogged. It would drop to zero for a while, then come back. If everything has been fine up till now, take the sending unit off and drill the inlet hole slightly bigger.
If you had zero oil pressure, the motor would already be in bad shape and you would be hearing a lot more racket.