Mazda B3000 Oil Pressure light

I have a 2000 Mazda B3000 that is having problems with cold mornings. When it is cold and I start it in the morning, the ol pressure gauge reads at basically nothing and the oil light comes on. There is definitely the right amount and type of oil in the truck, and once it warms up the pressure goes up and the light goes off. Sometimes the gauge fluctuates back and forth while it is warming up.

Would this be a problem with the oil pressure sensor- or should I be shutting off the engine withing the first couple of minutes when the light comes on?