When my boot latch stopped work it behaved similarly to this, the switch was fine, but the actuator was failing, sometimes driving would loosen it up enough to operate, othertimes nothing, taking it apart and cleaning/regreasing gained me about 3 months of "fixed" until it did it again.
Been 2 years since I changed the part and no problems since, worth noting if you do change the actuator, there are 2 types of actuator, I don't know when the crossover was, but I assumed when BMW gave the electrics and sprouse up. The connectors and mounting brackets are different between both types, so make sure you get the right one.
[Edit: And Land Rover Dealers don't carry the part anymore, I think it was a legacy thing from Rover since the part numbers match a the part for a Rover 75, but not quiet the same (could buy one to cannibalize maybe). The Dealers told me to check eBay]