The lack of evidence could be because the British never occupied Timbuktu and no British person even visited until the late 19th century.
It was ruled distantly by Morocco,  until it was incorporated into the French colony of Mali in the 1890s. There are extant description of Timbuktu, which seriously declined in size and influence after the 1600s - due to its scholars not being in favour with the king - and none of them mention flush toilets.