As always remote diagnosis is tricky and we need some more information.
1) Any chance of
a) A photo of the face of the relay with the pins on.
b) Notes of where the wires go to if you can work any of them out
c) A model number of the relay.
2)At least one of the wires should have a
fuse. Trace each wire back as far as you can to see if you can find any.
3)It helps to know if you have a pressure system or micro switched taps.
3a)Trace the water pipe from the tank to the pump. Can you find a water pressure switch ?
3b)Look at the bottom of all your taps, can you see any wires?
Very basic synopsis of how a relay works in case you don't know.
Apologies for the over simplification for any experts reading this.
A relay is a device that tests for a current in a (input) circuit and when it detects current closes a switch to provide power to another (output) circuit.
Usually the Output circuit is thicker wire capable of powering larger devices, but some folks use the same wire thickness so you can't rely on this.
e.g. The "input" (thin wire) terminals of the relay are in the water pressure switch circuit or the tap micro switch circuit.
When the water pressure is high this water pressure (or tap micro ) switch is open, I.e. no current flow
When the water pressure is low this switch is closed I.e. current flow
The "output" (thicker wire) terminals are in the water pump circuit.
When the relay detects a current in the pressure switch circuit it closes a switch (inside the relay box) on the "output" circuit.
i.e. provides power to the pump.
So a relay has four terminals :- two on the input circuit and two on the output circuit.
However, many terminals have a fifth terminal. For some applications this has a specific purpose but usually it isn't used. (but manufacturers just find it cheaper than making two different types of relay.