I get it too, but only heard it (first noticed it now) by gently pressing the pedal in the garage. In the quiet garage, it easy to hear, every time.
Sounds like the relay might be under the dash. I was about to explore a bit, when my neighbor started to mow his lawn next door. Then, I could no longer hear the sound. The trim part under the dash, under the steering wheel, can be difficult to properly reseat (the middle post near the door on mine was difficult to align and get back in), so explore with caution.
Never noticed the click before, on mine more of a low frequency thunk, possibly these relays have a range of loudness and/or sound, and I am old too.
If someone checks out the various parts pages, there is probably a relay called brake light relay, or some similar name.