I thought was a very interesting article, that highlighted India does not have any chance to play the Tibetan card at all.
The 17-point agreement signed between Tibet and China on May 23, 1951, ended any hopes of genuine autonomy for Tibet. Further, the signing of the 1954 India-China agreement symbolised the complete formalisation of all developments since the invasion of Tibet by China and the total elimination of Indian political influence in Tibet.
I read the 17-point agreement signed between Tibet and China on May 23, 1951 ->this agreement was signed by Tibetan representative then Ngapoi Ngawang Jigme in Beijing.
Interestingly Ngapoi Ngawang Jigme, was an officer of the Tibetan army, he seriously wanted to reform the army but faced opposition from the Gaden Phodrang. He fought on the side of the Tibetan army, before the Tibetan army collapsed in the face of an unbalanced opposition.
He was highly respected man by the Chinese leaders, during his funeral Hu Jin Tao, ex-general secretary Jiang Zemin, Wu Bangguo, Wen Jiabao, Jia Qinglin, Li Changchun, Xi Jinping, He Guoqiang, Zhou Yongkang, etc. This shows that he was highly esteemed in China.
If one is interested to know more about why India can never really play the Tibetan one can read the links below :-
Seventeen Point Agreement for the Peaceful Liberation of Tibet
https://en.wikipedia.org/wiki/Seventeen_Point_Agreement_for_the_Peaceful_Liberation_of_TibetNgapoi Ngawang Jigme
https://en.wikipedia.org/wiki/Ngapoi_Ngawang_JigmeFive Principles of Peaceful Coexistence
https://en.wikipedia.org/wiki/Five_Principles_of_Peaceful_Coexistence