When the Sudanese troops of the Uganda Rifles mutinied over conditions and arrears of pay, there were Sikhs among the forces sent to deal with them. The post-mutiny reorganised force had Sikh NCOs and 400 other Indians whose ethnic origins I'm unsure of.
I think it would be reasonably accurate to include a smattering of Sikhs wherever your game is set in British East Africa, they weren't confined to British Central Africa. The East African Rifles had 300 Punjabis on their strength at their peak. A photo shows them garrisoning Witu on the coast, and they also garrisoned the Jubaland forts on the northern frontier against Somali attacks.
Prior to the combination of all three forces into the King's African Rifles in 1902, the Indian contingent of the East African Rifles were sent home (I think in 1900). Not sure about their compatriots in the other two, I'd have to go rummaging in my books to find that out.