I haven't heard that technique specifically, but there are a variety of movements and postures suggested to patients while trying to elicit reflexes elsewhere in the body. The basic idea is to give the patient a new task and thereby distract them from suppressing the reflex. If they're watching you tap their patellar tendon with a reflex hammer, there's a subconscious tendency to tense up the leg muscles which can suppress the reflex. If you then give them something to do with their hands - or maybe their jaw - it will redirect their focus, there will be less tensing up in the leg muscles, and you can elicit the reflex. It actually works very well, and I suspect that's the aim of the teeth clenching.
Perhaps there is a difference between motor commands stemming from cranial nerves and those from spinal nerves that affects parasympathetic or sympathetic nervous control?