Ok there are two ways the water pump is controlled (or 3)
one is a switch, or two "3-way" switches this is the best controller..
The other is an electronic box with mulitple switches.. that controller can fail as it contains relays and such.. Same as a slide controller or step controller
(And I've two slide controllers fail) My guess is the clicking inside the wall is a failed controller. There may be an easy fix but alas that kind of design work I need to be eyes or hands on. But basically I'll outline And I stress this is a short term fix.
Remove power lead from pump. run a 12 volt FUSED lead TO (NOT CONNECTED) the pump area. Install a relay.. 10 amps capacity or more.. 12 volt low current coil
Hook existing feed to relay coil and other coil lead to ground (Make sure it's a good ground)
Hook hot wire and pump to relay contacts.
NOTE: Someone ask where you were measuring the 6.5 v
IF across the motor it might be a bad ground on the pump.