2001 volvo v70 tailgate lock/unlock relay location. Tailgate not locking checked fuses, no sound from tailgate, however do get click sound from fuse area.

Check the wiring to the rear hatch. The cables break and cause a variety fo problems like yours. You will have to take the plastic cover off and expose the cables.

Besides what is already mentioned, 2001 volvo v70 tailgate lock/unlock relay location
There is a fuse #8 in the rear cargo fuse panel that controls the rear door locks and fuel door Lock. there are a whole bunch of relays in the REM that control different functions. Is possible that one relay is faulty and blowing the fuse.
Remove relay RM1, that one controls locking Left rear door. If fuse blows again after you activate the door locks, then that is not the culprit. Replace the relay back to its place.
Remove relay RM24, that controls locking right rear door. Try activating door locks and see if fuse blows.
Next try removing RM20, that controls rear hatch door locking.
By the way, the numbering of the relays is under each relay

Also check for voltage (at the lock actuator) when key is pressed. If voltage is present, then replace the actuator. If no voltage, inspect wiring and relay / fuses again.