MotoTRBO uses "unsupervised TDM" for multiplexing. As a result, the subscriber equipment is dependent upon a synch signal from the repeater. If a subscriber keys up and can't find this signal, it sends a request to the repeater, when then issues the synch. During an exchange, and for a period of time afterward (which can be set in the repeater programming), the synch is continued, so that an exchange can be resumed after a short pause without the delay for the request/grant of synch. I believe the brrp you're hearing is the synch signal during timeout.
Edit: Motorola publishes a "Guide" to MotoTRBO (I don't recall the precise title), which is available on the web site. This is required (and interesting) reading for anyone venturing in to what is a pretty different world than most of us are used to.