Where did the kit come from?
Do the washers work as long as the button is pushed, or does it require a single presh & then the pump works on a timer?
I had factory headlight washers on an old Subaru I used to own.
It was wired up with a soft touch button on the dash & then had a timer which operated the pump for about 2 seconds.
Are you getting power to the pump when you push the button?
It could be a simple case of a plug coming undone.
Can you get a better description of what is (or not in this case) happening?