Since it's low-voltage (12V) and NOT mains power, flexible cordage is allowed broadly.
If you missed that it's low-voltage, the dead giveaway is the black and white cord wires in the photo absent a green/green-yellow equipment safety ground. Low-voltage DC doesn't need it.
You'll want to use a plug that is for 12 volts DC
First, polarity matters. Second, the standard 120V NEMA 1 plug is right out, because some epsilon-minus will plug it into a wall socket and it will blow up. I have thought of using sockets like NEMA L3 that are so obscure no one uses them, but conversly, no one sells them either at a sane price.
Honestly, there aren't a lot of good choices for 12 volt DC plug. The very ungainly "cigarette lighter" socket seems to be the de-facto standard, which just goes to show how desperate we are for a standard. Andersons are also ungainly and Molex are too hard to unplug. Coaxial connectors like on your Internet router is probably as good as it gets.
If you need outdoor/waterproofing, then hit up electronics supply shops for automotive grade sockets and plugs, with the little gaskets and all that. Or pull 'em off GM cars (the most common) at a u-pull-it junkyard.