Every Taal has its own rhythmic cycle as you have explained in case of Teentaal which has 16 beats with khali at 9th beat where you do not clap, claps are reserved normaly for the resonating beats, there are exceptions though.
For example in Dadra, which has 6 beat cycle, counted as: 1 2 3 4 5 6 Dha Dhi Na Dha Tu Na Clap count count Khali count count or 0 2 3 X 5 6
While practicing, I believe, one should count by hand while reciting the bols before starting to play it on Tabla.
PS: A kayda, I am sure you would love playing
Trkttak Dha Trkttaka Dhagena Tina Kadnak Trkttak Dhanaghena Dhati tinakina