L-jet fuel pump question Options

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I have a 1974 1.8

while the car is idling I can hear the fuel pump running (it is a non-Porsche part, moved to the front trunk by PO), however it isn't running consistently. I hear it wax and wane over the period of a few seconds. Kind of like a rotating tornado siren, only faster (and quieter (IMG:style_emoticons/default/smile.gif) )

So here is my question... is this normal, or should it be running at a constant pitch whenever the car is running.

If it is normal for it to wax and wane, what signal is telling the pump to slow down, then speed up again, all while under a constant load (parked and idling).

The reason I ask is that the fuel pump hasn't run for a year, and I just recently got it running (high resistance connection on relay board, subject for another post). Last year the car ran well enough to take out on the highway, but I thought I was hearing a continuous pitch from the fuel pump. Now the car cuts out on acceleration and struggles to go around the block.

Thanks