Feeling a little dumb here, but is the OEM washer a manual pump activated by pushing inwards on the right side column stalk? I've never driven my car in the rain or filled the washer reservoir, so that's news to me. Every day is a learning experience.
Just a thought, if that is the case, a neat upgrade would be a cheap pressure switch connected to the stalk pump to switch on an electric washer pump, probably through a relay.
Tom
[Correction] Oops, I missed BDA's post. Yes, I think my TCS has an electric pump also.