I do not have access to a "mut II" so I'll just run some theories by you.
The check engine light does not illuminate when the fault occurs. It appears to be a fuel starvation problem as engine tries to fire when an immediate restart is tried. So guess the controlling computer has not shut down the ignition.
I have checked that the fuel pump relay is making the electric fuel pump work. Swapped it with like relays and I can hear it ticking at restart attempt. Tried running with petrol cap off in case fuel tank vacuum a problem.
When the fault is about to occur, switching to air-con on loads the engine makes engine "hunt" and then die. A thinng fuel air mix just prior to engine "death" perhaps ?
Just waiting a couple of minutes the engine can be restarted and will run for several minutes before stopping again. The 2 minutes seems to be little time for any sensor to
cool off and one would expect any sensor to have a much longer hystersis period (or time out period).
So I am suspecting a fuel blockage that restricts the fuel delivery to the point where the engine dies then some how allows enough fuel past during the short "cool down" period.
Can you tell me where the fuel filter is located ? There is also another sensor I can see through the branches of the inlet (but can not reach), can you tell me what this sensor is.
Any other suggestions??