OK, there seems to be a little confusion on the speeds of the electric fuel pump.
There are only 2 speeds on the Cessna's, not 3!
Cessna's have a 2 sided switch "Low and High". Which works as follows: If the low side is switched on you will only get low boost! If both are switched on you should get Low if the throttle is pulled back and High starting at somewhere around 1/2 throttle.
There are a couple of adjustable resistors in the circuit as well as a micro switch that makes the fuel pump run at 2 different speeds.
The reason for the low and high is as follows:
If the engine driven pump takes a dump while flying. The throttle is pushed in so you need high boost in order to have enough fuel pressure to run the engine at a higher power setting.
If the switch is on the high position without the micro switch circuit and resistors if you pulled back the throttle (without a major mixture knob adjustment) the fuel pressure would be too high and possibly kill the engine.
So as you pull the throttle back the micro switch will switch you to "low" even when the high side is switched on.
That way if the resistors are set up right the engine shouldn't quit on you example: when you are coming in for a landing with an inop engine driven pump.
The low side switch is supposed to be for starting and low power settings.
On the early fuel injected models the low side didn't do anything if you switched it on until you are in the start position on the key switch, then it will only pump low.
On the newer models low pump will come on without being in the start position.
I'm not sure when the switching changed changed I think late 60's maybe.
(I always use the high side with full throttle for prime myself)
I have found that many planes are not set up correctly!
A quick ground check is with the engine off and full throttle and mixture, when you hit the high side of the switch your needle should get above the green fuel flow arc.
If it doesn't then you won't have full power if your engine driven pump quits!
