When I was a teenager I started to count bars rest using the keys of the left thumb on my bassoon. At that time I had an instrument with 8 keys for my thumb, and I counted 1 on the Bb key, 2 on the B key and continued anticlockwise around all the keys (see diagram). I still use the same method even though I have some more hardware for the thumb on my present instrument!
I have noticed two advantages using this method: