There's another HowTo on
how to do this at
Neons.org, but it has no pictures and isn't terribly
detailed. When I did it myself, following those directions, I
took pictures. I thought I'd make a more detailed howto on it.
First off, pop out the ashtray. It's a friction fit, so just pop
it open and pull straight out. It should slide out easily.
Then get your fingers into the gap in the bezel above where the ashtray
was, and pull gently and evenly. It just snaps on with clips, so
it should come off in a series of "pop" noises.
When it's off, you'll see something like this:

(Click For Larger Image)
The knob won't be missing when you first
pull the bezel off. Remove it now, it slips off just by pulling
gently on it. It's keyed, so don't worry about the
orientation. Then, behind the knob, you'll see this:

(Click For Larger Image)
Uh oh, lots of choices. We're
going to cut the third one down. To see what I mean, see this
obviously marked picture:

(Click For Larger Image)
To cut this, I used a dremel tool with a
engraving bit. This was the easiest way, you could also use a
drill with a drillbit, just be careful, as it's easy for the bit to
slide off. I tried this myself before going with the dremel and
making my life easier. Here's a picture of the cut completed:

(Click For Larger Image)
Note the attempt with the drill to the
right of the final cut, that's my drill attempt. The engraving
bit did a cleaner job. Cutting this lead disables the switch from
clicking the AC on. You can still turn it on manually, but we all
know how much the powerful AC system on the Neon kills engine
performance. It sucks to try to pass someone only to have what
feels like 40hp getting sucked down by the AC!
I'd reccomend using a shopvac or similar to suck up the shavings, then
test and make sure the AC doesn't engage when you kick the defrost
on.
Then just snap the bezel back on, pop the ashtray back in (just align
it and push it until it pops into place) and wallah, complete!
Much less annoying.