I had an inverter behind my seat for a long time - 1500 watt square wave that would do up to 3k for short bursts. Right behind the cab in a box is almost the same distance.
I had it fused to my group 31s, powering little things was no problem (tool battery chargers, phone chargers, whatever else). The only time I made sure to start the truck up was if it was a high draw device (heat gun, blow dryer, mini-fridge, etc...). It wouldn't be too hard to make a simple circuit that starts the truck whenever it gets below a set voltage, if similar products don't already exist? Power to the fss, momentary power to the starter until alternator voltage kicks in, maybe high idle?
My inverter was setup to turn off before draining the batteries too far down. I also used it with extension cords frequently. My tool batteries, even the biggest battery only holds maybe 175 watts or so (milwaukee 18v 9a) - not accounting for conversion losses for going from 12vdc to 110vac back to tool dc voltage, and the charger efficiency and other such issues.
Most group 31s have a 20hr capacity rating, I don't recall mine but I found a cheap one with over 100ah at the 20hr rating, that is at least 10 amps an hour of constant usage from two g31s - 120-130 watts an hour or more depending on the batteries. Most 12v tool batteries have much less capacity than that, as well as most 18V. Some have chargers that can run off 12v to save some conversion losses.
Also if you discharge faster than that 20hr rate you lose some of the capacity, if you discharge slower you gain some. Also most people recommend not discharging a battery beyond 50% for longer lifespan.
Another issue I didn't see covered here is square versus sine wave inverters. Cheaper inverters use square wave, some things can handle that fine but others don't like it - usually televisions from what I've seen. In general most things will consume more power on square IIRC. Sine wave inverters cost more for the same wattage, but provide the same power you would get from a residential outlet.
What do you hope to power?
