I got my H4 sockets in the mail today. They mate perfectly with the stock wiring, bypassing the bulb adapter. The difference between the H7 and H4 sockets are that the pins are a little further apart (13mm vs 16mm, respectively) and the pins are individually a little wider (6mm vs ~7.5mm). Also the H4 plug has a slot for a third pin, but that one's not used on our bikes (typically H4 bulbs are both hi-lo and that third pin provides power for that function).
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Edit: (H4 is on the left, H7 on the right)
Other than sheer laziness, I do not know why Kawasaki chose to use an H4 wiring socket, then go through an adapter to use an H7 bulb. Pure silliness