Im confused about a couple of things.
Is the pressure switch the solenoid that opens to allow water to get to the nozzle?
Is the shutoff valve just a manual shut off valve or is this the solenoid?
When you say its on and misting - you mean the its misting full time - no on/off with the solenoid?
If so, the pump is working the way it is supposed to work. It has an internal pressure switch that turns the pump off when it reaches the hi setting - which could be anywhere from about 60-150 PSI. There should be an adjustment screw somewhere on the pump.
Anyway, the pump will turn off when that pressure is reached, then it will turn back ON when the pressure drops to the lower setting.
There are two things you need to do to eliminate that cycling.
1) Add an accumulator tank.
2) Add a pressure reducer right after the accumulator tank and before the solenoid that controls the nozzles.
The pressure reducer should be set to a pressure less than the pump minimum pressure.
This is the one I used when I was doing HPA. Its cheap, but works well.
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This is the accumulator tank I used.
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Make sure the pumps max pressure is less than the accumulator tank max pressure. That tank is safe to 150 PSI, so you would set the pump to about 125 PSI, then set the pressure deducer to anything under the cut ON setting of the pump.
If you do that, your nozzles will always have an even, constant pressure, and your pump will only need to run every hour or more depending on the size of the tank, number of nozzles. Those pumps are not really designed to run full time.