There’s a computer involved with the pump motor. You press that button, and the computer detects the press and converts that to what’s called CAN data, which it sends to another module, and that module turns on a relay, which send battery power to the power terminal of the pump motor. The other terminal of the pump motor should be connected to chassis ground, so that’s something you can check with an ohm meter.
CAN is the name of the computer network used in cars. Sort of like LAN is the name for desktop computer networks. CAN defines the standard protocol for how the data is supposed to be interpreted by the various computers.
Both the front & rear pump motors’ power supply goes through a 10 amp fuse, so make sure both sides of that fuse are powered up with battery voltage when the pump motor is supposed to be able to work (usually that means the key is in the “on” position). Beyond that you’ll need help from a shop that has CAN-buss debugging capability.
There’s a customer interest bulletin btw on the ww pump system on that car. It’s about how the inlet screen can get clogged and what to do about it. You dealership can (no pun intended) probably provide you a copy. Ask about TSB BOD095.
If you discover you actually do have power to the pump motor, and you can hear it turn on , but it doesn’t squirt, that’s likely a clog somewhere. If it doesn’t turn on when powered up, either the motor is burned up (which you can tell by measuring its resistance) or it is stuck. I recently unstuck my Corolla’s ww pump motor using a waterpick device to clean it out and a few taps with a screwdriver handle to unstick the armature. Good idea to never let the bottle go completely empty, b/c for some reason that leads to the pump motor getting stuck.