starter makes car start, turn off shortly

If you tried starting it with the key left in the ignition, and that didn't work, then PATS isn't your problem here.

As far as that other site goes, I'm going to say that it's wrong, someone else can correct me if I am, but to my knowledge Passlock isn't used in Ford vehicles.  From what I can see DEI's reference chart doesn't refer to the 555L for any Ford vehicle.  You don't need it if the car isn't starting with the key in the ignition.

Perhaps, it's possible that that second wire is controlling more than the heat?  You might want to try connecting that now and see what the outcome is since you'll need to do it anyway.  Remember not to just connect the 2 wires together but you'll need to use a relay.

This document: http://www.designtech-intl.com/pdf/notes/note234.pdf

has a good diagram for how to wire 2 ignition wires from just one output.  Don't pay attention to anything except the first diagram on the page, as the rest of it is irrelevant to your particular system.  The diagram you're looking at has the one wire coming out of the box that says "DesignTech" and going to two relays.  In the box that says "DesignTech," just imagine that's your Commando remote starter system and where is says "Green Ignition 2" that's your PINK ignition wire from the Commando.

Apart from that, all I can say is have you checked the tach wire lately?  Are you sure it's making a good connection?  Make sure you aren't using TTAPS.  Some people here swear by them but I haven't had much luck. 

Does the remote start system have any way of reporting what the failure was through the LED, flashing lights, chirps, maybe?  I know my DEI Viper system can flash the LED, but I have not been able to get a lot of information on the Commando system.  If you know the manufacturer's name, please post it and I'll try to get what I can on it.

Aha! That explains it then. The Code Alarm website says that one of the Gray / YELLOW wires is ignition and one is accessory, though. They fail to mention the BLACK/ Green wire but the OP does mention it.

I would strongly suggest testing each of these with a multimeter.

Accessory Wires have voltage when the key is in ACCESSORY or RUN positions.  The voltage usually drops or goes away completely when in the START position.

Ignition Wires have voltage when the key is in the RUN or START positions.  They don't lose voltage or power in START.

Starter Wires only have voltage when the key is in the START position.

All wires have no voltage when the key is in the OFF position. The ones that do have power at this time are your constant 12V sources.

Make a note of the wire's color and how it behaves during each key position. Now you'll know which ones need to be connected to what lead out of the remote starter. Reference the document above to see how to connect more than one wire to a single output using the relays.  You can get relays at auto parts stores.

Use a digital multimeter.  It's safer on the car especially if you find that you need to test wires that are part of the car's sensitive electronics.

Yes, Tach=Tachometer.  When testing this wire you'll need to put the multimeter into AC voltage mode, and keep in mind that it should fluctuate when you rev the engine.

T-Taps (which I had written in all caps) are a type of connector that is sometimes used by installers in automobile wiring.  There's a whole 4-page thread that cropped up on here not long ago where people are debating wether they're any good or not.  Some people swear by them. Personally, I haven't found them to be that great.  Your mileage may vary.  I would suggest that if you used one of these, try using some other method of connection and see if that works out better for you.  A T-Tap is a plastic connector with a metal "fork" that you fold over the wire and snap down, then you crimp a connection on the other wire and "plug" it into the plastic peice.  Don't confuse it with Scotch-Locks; they're similar but not the same.  If you don't have a clue as to what I'm saying a quick Google search should find some pages with a pictures of these.

If the remote start system tries to start again than it knows that the engine has stopped (or it at least thinks that it is) and it shuts down and tries again. If you push the brake it stops trying again because the brake is a shutdown trigger.

On my Viper system, you can find out what made the system shut down last time.  You hold down the program button, turn the key on-off, then let go, and the LED will flash 'x' number of times.  The manual tells you what the flashed code means.  Obviously, this method wouldn't work with your system but there may be a way to find out if you look in your manual. You'd need to let the system run all 3 times without interrupting it to see what it says. You may also want to re-learn the tach signal just for good measure.