The light comes on when the car stalls because the engine is not running and the pump therefore is not pumping. The pressure will always be 0 when the engine stalls and the light is directly related to pressure. This is normal, you have no problem, other than the engine stalling.
Then you need to have code checked, you can diagnose from there.
the sensor is going out
engine stalls sometimes driving
you can disconnect the negative cable at the battery for at least 30 seconds. if the problem is intermittent, the light will be out afterwards. if it comes right back on, seek a shop that does engine diag.
take it to a mechanic
why do check engine light comes on
idle air control valve (iac) could be dirty or clogged.
replace the alternator
If the "check engine" light is on, use a code scanner to find out what's wrong. You can borrow, rent or buy a code scanner from most auto parts retailers. Sometimes they'll even show you how to connect it and how to read the results.
The flaps that direct the air are moved by the engine vacuum, it sounds like you've got a vacuum leak somewhere.
It means your engine needs attention.