https://newskybox.sky.co.nz/tech-specs

It runs on a 12V barrel jack, so you could probably jimmy something up easily.

Automotive systems run on a nominal 12v DC. The voltage can vary anywhere between 10v to 15v depending on whether the vehicle is starting or charging. There can also be high voltage spikes due to the inductive components in a vehicle, eg relays, heater motor, wiper motor, etc.

I would be reluctant to connect an electronic device not designed for automotive use directly to the vehicle battery.

My suggestion would be a pure sine wave 12v-240v inverter.

Jaycar have this one on sale   300W 12VDC to 240VAC Pure Sine Wave Inverter - Electrically Isolated | Jaycar Electronics New Zealand

It may not technically be necessary, but a buck-boost converter could be used to give you a clean 12V supply from 10-15V.

There are power supplies made specifically for in car use, including ATX power supplies for computers. You could use an ATX power supply with a jumper on the relevant pins so it turns on automatically. If they're clean and powerful enough to run a computer, a Sky box should be fine. Plus, you'd also have 5V to play with.

The most likely problem could be if you run the car motor to charge your caravan system. Automotive "12V" can vary over a wide range and may have major spikes, particularly under load dump conditions. So if you were charging from the car system and, say turned the headlights on / off or pressed the horn button, you could have a problem. A DC-DC converter should smooth things out.

If you only charge your caravan battery from a mains supply, there's less risk but the voltage could still go to 15v or so. The skybox "will probably" be OK with this, but it is outside the normal operating range.