Sounds like either the windshield seal if defective or the heater core is leaking Check to see if water? is antifreeze
Sounds like heater core is leaking
The pipe that runs under the back rear of the passenger side of a 196 Pontiac Grand Am is the water pump. If there is leaking under the passenger side, the first thing to check is the water pump.
If you have your air conditioning running it is the moisture that is pulled out of the air when it is being cooled. That water is then expelled outside of the car
Have your heater core check out. On my navigator there was a leakage in a tube under the passenger fender. Take it off and check out you tubes.
It's the coolant control valve for the heater core that's leaking. It's under more pressure when the engine is running and that why the leak is more noticable.
you probably need a new thermostat, remove the one you have then get a new one asap.
This is either the heater core leaking coolant or the air conditioning drain line is plugged. If the water tastes sweet on your tongue or is warm it is from the heater core.
If it is water it is probably the condensation drain plugged up with crud. If it is engine coolant it is probably the heater core leaking.
Could be that you need some welding done underneath, but could also be the heater matrix. On most cars, that little box of tricks is buried away in the dashboard which needs complete dismantling to reach the blessed thing! If the water spells like antifrreze, then the heater core may be leaking. If it is just plain water, the drain for the air conditioning is plugged up. There is a hose that you can reach from underneath the car that is right under the heater-a/c unit and the hose can be cleaned out with a short piece of wire of even a straw.
IT is underneath the car directly under the passenger side
It can be one of 3 things. My first guess would be a leaking heater core considering the area where it is leaking. Are you sure this is water and not coolant. If it tastes sweet or is slick to the touch, it is coolant and you have a leaking heater core that must be replaced. Secondly it can be the windshield seal that is leaking. And 3rd it may be that the drain holes below the windshield cowl are stopped up allowing water to enter the passenger compartment.