Hi,

Usually the pump makes noise when it works. If no noise whatsoever locate the pump at the bottom of the washer reservoir. Disconnect its electrical plug and test for voltage (ask someone to pull the wiper stalk or tie a string from it to the steering). If there is voltage then the pump has issues.

There a separate pump for the tail gate. Located next to the windshield pump. Same troubleshooting as above.

Usually there nothing wrong with the wiring as the wires are stationary (unlike some wires going to the engine). The electrical plug's contacts may be corroded if the silicone/rubber insulator has disintegrated. Clean it too. Dab some dielectric grease for protection.

Haven't dismantle any washer pump before. Other members may have tips on this.

Amarin.