I actually used to do something similar with my radio equipment. A bit much for the cigarette lighter (usually rated at 10a not 20). So I just parked the car, set up the aerial and wires straight to battery.
For clarification, my radio has inline fuses right at the start of the positive and negative wires. If you've ever seen wires melted into people's carpet because they didn't have a fuse on their hardwired car electrics... Yeah.
And a truck is likely 24v, so twice the power for the same current. It's also not unheard of for trucks to have high power devices like inverters in the cab, so may have much more current and power available.
12v car battery and alternator is more than enough. The limiting factor is the fuse and/or melting wires. Thats why giant 1000w subwoofers use thick wire and larger fuses directly from the battery.
After googling i found numbers like 1200 to 2400 watts being produced by a car alternator. Just bridge the fuse and you can make pancakes in your car happy and without worries.