I believe the pump on the 1604 is the same as on the 1204, if so the pump is a very simple system and taking it apart to clean it will not help. The two connected tubes that go into and out of the pump is one tube that makes a loop in the assembly. The best way to clean them out would be to disconnect the hoses from the connector that goes to the bottom of the maintenance station and use a syringe filled with cleaning solution to spray threw each of the tubes. Also unless things have changed, you can not replace just the pump, you have to replace the entire maintenance station, I tried finding replacement hoses for mine when one of my houses got a small pin hole, but I couldn't find any that would work.
Look for the two tubes that come out of the bottom of the maint station, there is a connection there where they feed to the waste bottle. That plastic connector has a very small inside diameter that may have dried ink in it. You need thin wire or a pin to clean it out. As mentioned above I doubt the pump is out on one side