This is from memory as Im not staring at a epson right now but....
From front of printer, remove right cover, there is a sensor that reads the position of a gear that drives the pump, basically telling the printer where the start of the pump cycle is. Mechanically the gear can get stripped, junk can get in there, it can get jammed, or the sensor can get out of position. Electically the sensor can die, the wiring can fail, or the main board can go bad. Epson service menu has a test section that will tell you what all the sensors are reading so you can tell if the sensor is behaving and the correct home position is set on sensors that need it, IE carriage position. Can't recall if there is a reading for the pump gear sensor though, and it might be one of the sensors that stops you from even getting into the service menu.
We have a huge day tomorrow but if I remember I'll try and take a picture of the parts in question. I know it can seem tough but epsons really are very simple once you get inside their head so to speak. And I hate seeing perfectly fine machines go to the landfill for want of a minor adjustment or part. I can only imagine the mountain of old cell phones and keyboards that must exist somewhere.
It never hurts to have two of everything in this industry.
