Hold on to the Pats thought for a moment. You said the engine will run when you spray (TB or brake cleaner) into the throttle body. Does the engine continue to run, or do you have to keep spraying short bursts to keep the engine running? Now, onto the PATS. Did you take the PATS module or are you still using your original ignition switch and key etc? I have some thoughts on this one. If the engine starts after you spray a short burst of (BC or TB cleaner) and then continues to run WITHOUT spraying any more, then you almost certainly have a PATS problem. The engine/PCM in a 2001 Mustang has a type C PATS system and does NOT disable the starter circuit. In this type of system, engine control functions will NOT be disabled if the engine has been running at least for 1 or 2 seconds. The fuel injection circuit is enabled after 1 or 2 seconds of engine rune time WITHOUT a programmed PATS key. This would explain why the engine would start after spraying into the TB....that is if the engine DOES continue to run after spraying. If the engine refuses to continue running after the first spray, then it is NOT a PATS problem. Any engine stalls or performance issues after the engine runs while the key/ignition switch is left in ON position is NOT an issue with PATS system.
Now, if you did not take the PATS module, then this would be a whole new issue. Does the THEFT light in the gauge cluster turn on or blink?
This is NOT a cam sensor problem. The engine WILL run with the cam sensor unplugged, just wont be as speedy of a throttle response.
This should help give you an idea of what could be going on....and that is an IF.....