I'm pretty sure this problem has nothing to do with the ignition switch.
It's temperature related because it only occurs after the engine
has had sufficient time to completely warm up. Previously what
would often happen once the engine was warmed up is that
it would start idling rough when not moving, and sputtering
out when accelerating in low gear. Now it just dies before
any of that starts to happen. So whatever component is
failing, is only doing so when it heats up.

 

Also just to clarify, the behavior of the instrument panel is the same
*** it's always been. when it stalls, only the battery light, and the oil light
come on.

 

When the car stalls and will not start.

1. Do you hear the fuel pump prime when you first turn the key to the II position?
2. Are you not getting spark?

 

yes I can hear the clicking sound of the fuel pump every time.
I just replaced rotor, cap, and coil and the coil is getting power
when I test the two wires feeding it. It's a brand new coil so
I'm sure it's producing a spark.

 

It only stalls when it's in neutral slowing for a stop sign
or standing still. Could it bee idle adjustment?

 

A partially open EGR valve can cause the engine to stall at idle. The valve is controlled by a vacuum hose. If you disconnect the vacuum hose and plug the vacuum hose with a hose clamp or spark plug, does the car stall out?

I would not recommend replacing the valve, because the vacuum controls could be messed up. The other thing you can try is to put a vacuum gauge on the vacuum tube to see if it is pulling vacuum at idle (it shouldn't).

 

I'll try to check the vacuum hose. But I want to re-stress the fact that this a
temperature related issue. It never happens when the engine is cold.
Only after it warms up. And it's loosing oil at a steady rate.

 

I was looking at the underside of my vehicle and I happened to notice that
the tube with ridges along it's surface that's connected to the muffler,
which I guess might be the cat. con. ? has a small hole burnt into the side of it.
Could this be the ultimate source of all my problems? as in, rough idle
surging when shifting up in low gears, which was what was happening
before the stalling.

 

Any idea what this thing is?

It's been dangling under my dash since I got the vehicle. It has six wires coming
out of it but two of them are cut.

And here's a picture from the underside I took yesterday.
How should I proceed?

 

The tube with a hole is a flex hose for your exhaust. The flex hose can just have a hole in it and creating an exhaust leak.

I am not sure of that part hanging from the dash. Is there anything identifying on it? Where do the wires (cut and intact) go to?