I may be way off the mark here (perhaps @jsocolar can put me right if that is so) but I think that using observation time as a weight would result in something closer to what you have in mind (and to how 1/5 differs from 100/500 in a binomial regression).
behaviour_time/observation_time | weights(observation_time) ~ ...
Potential caveat: trials are independent events. If what I say makes sense, it should be in the case when the total time of extractive behaviour is accumulated over several independent extractive events which are more likely to be observed over more extended observation time.