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For a possible reason, Encyclopædia Britannica says this about Bakht Khan (emphasis mine):
Related on his motherβs side to the ruling house of Oudh (Ayodhya), which was deposed by the British in 1856, Bakht Khan served for a number of years as a field battery commander in the army of the British East India Company. When the rebellion broke out in May 1857, he led his troops to Delhi, where he emerged as the dominant figure in the independent Indian government proclaimed by the rebels.
Wikipedia article on the Oudh State:
On 7 February 1856 by order of Lord Dalhousie, Governor General of the East India Company, the king of Oudh was deposed, and its kingdom was annexed to British India under the terms of the Doctrine of lapse on the grounds of internal misrule.
Wikipedia on Indian Rebellion of 1857 (causes):
After the annexation of Oudh (Awadh) by the East India Company in 1856, many sepoys were disquieted both from losing their perquisites, as landed gentry, in the Oudh courts, and from the anticipation of any increased land-revenue payments that the annexation might bring about.
Definitively not an answer, but info about Bakht Khan seems scarce (a simple Google search now returns this page as 9th result).
Upvote:-1
I think General Bakht Khan the Great was a disciple of Maulana Sarfaraz, who was a mathematician and a master of astronomer. Both were followers of Shah Ismail Shahid.
He advised his disciple, the General, to support the Heretic Bahadur Shah of Delhi.