don't know if this will help but just a little more info on this...
I've had the same issue and wiggling the connector would bring the pump to life (also found out while car was on the dyno and tuned by Bob). We've concluded that it was loose connection on the pump side (originaly thought that it was the plug & that it has a piece broken off). Well, few days later I lowered the pump (without disconnecting the hoses) and pulled the back casing of the electric motor off - and immediately saw the problem. The brushes have been so worn down that they did not make good contact on the slip-rings, and the dust from them was making a short (not sure why the fuse was not blowing). So, I cleaned out the dust, readjusted the tension on the spring that pushes the brushes against the slip-rings and my IC pump works like a champ again.
Not saying all this work was worth it, but you might also have the same issue. Btw, this was on a car with 44K miles (pump is the original one I am pretty sure).
We were pretty sure that it was the connector and wiggling it would make the pump come on (though I had to keep the connector pressed). This connector sits on there pretty loosely and mine looked like it has a piece of it broken off (oval piece missing at the end). But, it is actually the way that they are designed.
Just some food for though. And, also it is very easy to pull down the pump & look at it. There is only one bolt that needs to be removed and the pump can be lowered. If you jack up the passenger front side of the car, and turn the streering wheel all the way to the left - there is plenty of room to work with.
Hope this helps.