Poolman:
The pump vibrateds a bit then starts making the appropriate sounds.
This tells me it is getting a GO signal from somewhere.
My wiring book shows only one device in the power path besides the fuse and relay.
It is a round thingy with two wires going to it and called an Actuator".

Maybe that is what you mean.

In addition there is another round thingy that sits up above the shield over the exhaust manifold. Ih has what looks like a blue vacuum hose going to it and a big hose going out to the pipe that disappears into the shield.

However this is not an electrical part.

Is the pump supposed to vibrate before it starts pumping air?
Does this mean the thingy above the exhaust manifold shield id slow to react?

-- S'V' not wanting to throw parts at it.