It seems like it would be better to me to have something battery powered to take to the device rather than expect the seller to let you take it out to your vehicle where you have a power inverter and AC powered supply.
What I would do, using parts I'm familiar with, is start out with an 18V cordless tool battery I already have, then look for the cheapest host case (tool) for it, whether a new flashlight or something broken "for parts" on ebay or used at a pawn shop. This gives you not just the case but the battery interface.
I'd stuff something like this buck regulator module in it, add a short length of wire and whatever connector you need for the set of multiple plugs (like those you linked) use, and add a switch to reverse polarity. The module below is rated for roughly 4V loss so a fully charged 18V tool battery (@ 21V) would give you 17V out for a brief period or 16V and below for much longer. It's 5A continuous or 8A short term (till it heats up).
There are probably cheaper sellers of this module, I'm just linking it as an example of type.
There are also cheaper buck modules, with just a little potentiometer screw, or without a display, and they're smaller too, but a bit more fiddly to use if you need a screwdriver and/or multimeter every time you want to change the voltage, though digital panel meters aren't very expensive, you could just mount one on the casing.