Fuse 31 IS a good source of switched ignition. The camera would run fine on a 5 amp, probable a 3 amp.
You can fish the wire thru the back of the fuse box, it will come out behind the fuse panel for the lights (driver's end of dash) and you can take it from there.

If this is too frustrating, you can always take it to a car audio shop and get them to wire it up, if you have the rest of it installed, I'd think they'd only charge $25 or so.
A full install would probably run $50-60 or so.