It is sounding like an electrical, amperage issue. When the winch is placed under a load and the amperage and voltage is not sufficient, the solenoid starts clicking.
Things to check
- Battery not fully charged
- Circuit breaker weak or needs replaced.
- Check all electrical wire cable connections
- Make sure only factory wire, AWG size is being used between the battery and winch.
- Check Ground and Battery cables and connections.
- Lastly, if all the above has checked and are OK. Could be the solenoid
- How old is the winch and how often has it been used.