From memory, the centre orange light on this vehicle indicates whether the locking centre differential is engaged or not. When the light is on, the diff in engaged. When it’s flashing, it’s in the process of engaging electronically. For this process to occur, the main transmission needs to be in neutral, so trying to get the vehicle to move and change gears while the diff is somewhere between engaged or disengaged, might be the problem.

I’ve also heard of problems with the sensor that detects whether the centre diff is engaged or not on this make and model. Sometimes the sensor can die, other times it’s just a wire that has fallen off, but it could mean that the vehicle is confused about what to do and the transmission is stranded in neutral as result.

Try rolling the car forward a few metres (if possible and safe) to see if that small amount of movement allows the diff to engage and normal operation to be restored.

This sounds – on the surface – very much like a problem with the car’s body computer. The body computer controls all the electrical functions you’ve just listed as well as potentially being responsible for controlling the immobiliser. If the computer isn’t telling the immobiliser to switch off, you could easily find that the engine will turn but not fire.

It doesn’t work every time, but one way to reboot the body computer is to disconnect the battery and leave it overnight. This will sometimes restore the computer to factory settings (for want of a better term). If the computer is on the way out, however, this reboot may not be permanent. The other thing to check is the battery inside the ignition key. A flat or weak battery here can also mean the immobiliser doesn’t switch off and the engine will refuse to start. If none of that does the trick, an auto electrician is your best bet.

Even when it’s completely empty, your caravan is still likely to weigh a couple of tonnes (give or take). At which point, you’re using a fair chunk of the Pajero’s towing capacity of 2500kg. What’s happening is that the transmission of the car is choosing to shift down a gear or two to bring the engine up to a speed where it’s making enough power and torque to haul the rig along at the speed you’ve chosen to travel at. Maximum torque in the Pajero’s 3.5-litre V6 occurs at 3500rpm, so that’s what the transmission will aim for when you need maximum thrust.

The process also takes some of the load off the transmission, helping it live longer and avoid damage and overheating. There’s a general rule that says you shouldn’t really tow anything remotely heavy with the transmission in overdrive. Experienced towers physically lock the gearbox out of overdrive, and this, essentially, is what the car is doing for you by shifting down gears when a hill or headwind increases the load on the driveline.

The petrol V6 in the Pajero was never a fuel sipper, and I’m not surprised you’re seeing higher fuel consumption in this scenario. This is also the reason many people who regularly tow choose a turbo-diesel to do so.