Needing a simple circuit to switch a vacuum pump from a pressure switch at 4.5v
The switch you're using has very little hysterisis, which isn't great for you, but you can still make it work. There are many different ways to do it, but I would say that the simplest is to use a schmitt trigger and some capacitors:



simulate this circuit &ndash; Schematic created using CircuitLab
What happens here is that the motor stays on until the target pressure is reached. At the target pressure (when the pressure switch activates), the motor will immediately turn off. The pressure switch will then deactivate and after about 7 seconds, the motor will turn back on until the target pressure is released, and so on. If you wanted the motor to continue for a bit after the target pressure was reached, you could change R1 to 10k and add a 100k resistor (R2) inbetween C1 and M2/R2. To increase the size of the delays, increase C1, or increase R2 (if you added it), or increase R1 (if you dont have an R2).
There are a few issues with this, mainly that the delays will change as the battery voltage changes (and as the temperature changes). The delay also wont be very accurate generally, as capacitors have quite wide tolerances, as does thie schmitt trigger.
If you really needed something more precise, it would probably be easiest to replace everything except the pressure sensor, M3 and D1 with a simple microcontroller.