I'm pulling a 16-foot Coromal pop-top caravan. It’s not heavy and not loaded. The car is a 2002 Mitsubishi Pajero Exceed petrol which seems to rev at a constant 3000rpm, even on open and relatively flat roads. It drops back when level or on decent. Is it normal to rev at 3000rpm, and constantly vary what gear it’s in? It’s making fuel consumption higher than necessary.
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.