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Whats wrong with a contact switch on a scale ?
Convert the pressure sensor output to a Varying Voltage then use a Comparator IC (LM339 is an old one) to drive a transistor switch.Really this is very easy and has been done long before micro-controllers were available.
Only you will know whether a FSR will be sufficient for air pressure. If the pressure differential is large, I would expect it would be OK.I would use an opamp rather than a comparator. I've found a comparators like the 339 to have a larger transition zone than an opamp set to 5000x amplification. The transition zone, in turn, is somewhere where your device may be half-triggered, which is bad.You probably want to clean that up with a Schmitt trigger, too.
That being said: If you use a comparator, or opamp, you're already worrying about a DIP-8 socket and supply voltage. Why wouldn't you use something like an ATTiny85 in the same form factor, with an ADC, and some digital I/Os? The Tiny will run at 1 MHz or 8 MHz clock without any external components.
Seems like it should work to me. I'm used to VCC-to-GND opamps, where GND is the most-negative, but if you have a symmetric supply (-12V available) then that looks legit.