To run an inverter, you need to do some math. A 1200 watt AC inverter will draw 100 amps pf DC power, and only supply 10 amps of AC power. At least that is how it works on paper, need more amperage in the real world. Let us know the amperage draw on the mattress pump, and multiply by 10, that will be the minimum current draw on your 12 volt outlet. Using a cigarette style is good for 30 amps at best.
Here's a test. Get your inverter, plug in to your truck lighter socket, parked near your camper, run an extension cord to bedroom and power the pump. Let us know how it worked.
Want the equations; Watts equals volts time amps.
1200 watts at 12 volts equals 100 amps
1200 watts at 120 volts equals 10 amps
AC volts, or DC volts doesn't matter, a Watt is a Watt.
You need 10 times the 12 volt DC current to run a 120 volt AC device,
(not counting losses in the inverter).
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