Hi! I know you have a new pump etc, so this may not apply, but for anyone else stumbling upon this topic it should prove useful.
I recently fixed my washer bottle pump, and I haven't seen any posted relating the the repair of the actual pump. The below worked for me but I can't necessarily guarantee it will work for everyone.
It involved removing the pump from the bottle, breaking open the top cap to get inside the actual pump. I noticed that the little centrifugal magnet, were stuck to the impeller. I wiggled them back and forth to free them, and strayed with contact cleaner before leaving them to dry.
Put the pump back together; connected to a 12v source and it whizzed away. Its been fine ever since. See below.
1. I removed the pump, connected my voltmeter to the connectors for the pump. Pulled the washer trigger and the voltage showed 11.7v so I know I am getting power at the pump. Isolating the problem to the pump.
2. Bend the small plastic tab on the pump top cap back, this is quite flexible. This will allow you to twist the top cap with some grips, and break the seal, and take of the top dap.
3. There are two small magnetic blocks on the inside of the lid which when supplied with a voltage put against the copper windings on the impeller shaft, turns the motor and spins the pump. Basically a very simple little motor.
One of the small blocks was damaged, but still servicable. I blew the broken bit out of the motor housing with compressed air.
4. I then cleaned up all the contacts with contact cleaner and left to dry.
5. Then hook it up to a 12v source, or simple plug back onto the power cable on the van (don't bother reassembling it into the bottle at this point in case it doesn't solve the problem. I heard to motor spin, and sounded powerful.
So I reassembled everthing, sealing the pump top cap with a some delicately applied clear silicone. Put the bottle back on the van with some new U-nuts and zinc plated bolts, put some new fluid in, turned the key, pulled the stick, and the front of the van was covered in blue stuff.
All Good!. Its been fine since which has been about 30 pulls of the washer while out and about.