I am sorry to say that the only times I've experienced it is on runs significantly longer than 5k (10km+). Of course, everybody is different and perhaps that's related to my relatively high fitness at the time (why would the mechanism kick in at a universal distance, rather than your personal point of pushing past exhaustion). But I don't recall feeling it when I first took up running (it felt awful!) but at some point it started to happen occasionally. Due to injuries, illness and whatnot I didn't run much for several years so I'm now back roughly where you are, and I miss that feeling!
I am sorry to say that the only times I've experienced it is on runs significantly longer than 5k (10km+). Of course, everybody is different and perhaps that's related to my relatively high fitness at the time (why would the mechanism kick in at a universal distance, rather than your personal point of pushing past exhaustion). But I don't recall feeling it when I first took up running (it felt awful!) but at some point it started to happen occasionally. Due to injuries, illness and whatnot I didn't run much for several years so I'm now back roughly where you are, and I miss that feeling!