Hi Frank,
I had rebuilt my original BJ8 pump-type washer many years back and, although successful, found it a waste of time as I expect to rarely be in a situation that would require its use. When looking for a place to put my driving light switch I decided to make the button useful and installed a push-button switch inside. Now I have a useful item on the dash that keeps the look of originality and have never missed the loss of a windshield washer.
I am sorry for not addressing your request and did use the washer when the Healey was my every-day car; however, even then I felt that item to be useless. I would suggest not rebuild or replace the pump and install a push-button switch inside with an electric pump as Randy has done.
All the best,
Ray (64BJ8P1)