Well, he might get his little hand in there, but there's no room for a wrench.
I noticed the serrated edge of the "washer" on the vertical adjuster, so I stuck a flat-bladed screwdriver in there and twisted it. The washer moved and so did the headlights, but the plastic headlight fixture got chewed up. It's a good thing I don't have to do this often.
And I still haven't found the horizontal adjuster, but I don't need to, so far, so it doesn't matter yet.
Somewhere in Kawasaki there's a product manager who decided not to spend the money on more accessible adjusters. I've been in meetings where this sort of thing is decided. At the end, someone always makes a joke about the customer, something along the lines of "F__k 'em if they can't take a joke."