Firstly...highly unlikely to be a Becm problem.
Could be that either the tailgate pushbutton is wet/dirty/corroded. Being at the back they tend to vaccum all the ****e and damp up over a period of time.
The lower taigate carpetted panel has to be removed to access the switch which is a normally open, 2 wire switch operated directly by the pushbutton. The panel is held by a few plastic fasteners along the bottom edge and are hidden by the hinged plastic drop down plastic flap. Release and lower the rear seat(s) for access, climb into the "Boot", prise the flap forward to access the fateners and release them. Now get hold of the lower edge of the carpetted panel and pull it away from the tailgate, now bend the panel whilst pulling it away and when it is clear at the bottom, pull it downwards out of the top plastic trim just under the upper edge of the lower tailgate. You will see the rear of the pushbutton which is held by a couple of self tappers, you will also see the plug with two wires. Remove this plug and jump these two wires together, the latch should unlock. If it doesn't, the problem is either the latch motor/solenoid or a wiringh problem.
Remember that the majority of switching on the P38 is on the negative side of the circuit and not the positive with the negative switch feed coming from a wire connected to the body and the live side of the component being fed via the Becm/ fused circuit.