>>does a lack of response indicate that I am correct

I don't think so. Over a few compression cycles, the reading on the gauge goes up from zero - thets just because you take some air from the cylinder to pressurise the pipe and gauge - the one way valve in the gauge tip prevents it all just leaking away between compressions.

As the pressure in the pipe and gauge nears the peak pressure in the cylinder, a smaller and smaller volume of air passes from the cylinder, via the one-way valve to the pipe and gauge.

Eventually, you reach the equilibrium situation where the gauge doesn't move much as each compression passes. However, this pressure isn't a sum over a number of compressions, it's just an approximation to the peak pressure reached in the cylinder, and as such, is representative of the peak pressure in one cycle, and this isn't in any way a sum, or an average pressure.