Assuming the equipment is in a standard configuration, skimmer, pump, filter, returns, with the pressure gauge reading the filter INLET pressure. I also assume you are using filter sand.
I've seen similar bahavior, although not to the degree stated with the pressure rising 18 psi, if the filter has trapped small particles. I've seen it after adding DE to a sand filter. Almost like shutting off the pump momentarily allows the fine stuff to 'float' again inside the filter. After operating for a while this small stuff cakes on top of the sand and causes the pressure to rise. An 18 psi rise seems a bit much though.
When you kill the pump do you see any backward flow out the skimmer? My thinking is a big air bubble in the filter that is compressed while the pump is running and going back to atmospheric pressure when the pump is turned off. This could cause a lot of churning in the filter. Much more than if there was a solid charge of water. Filters are normally designed to bleed off any trapped air.
Best thoughts for now.
Al