On automatic transmission PTOs, the PTO clutch-pack is supplied oil under pressure from the transmission when 12 volts is applied to a solenoid valve mounted at the PTO.
On 2000-gallon water trucks, this power comes from the switch through an inline fuse between the switch and the battery.
4000-gallon water trucks with air controls in the cab, the 12v comes from an air contact switch at the battery with an inline fuse.
The air control in the cab closes the contact switch supplying 12v to the PTO.
In both cases, you must adequately ground the solenoid ground wire. The contact that turns on the PTO light is a grounding switch that closes when oil pressure is present, turning on the light.
If the light is on, the solenoid is working.