Then the 5th Regiment LC becomes the 105th Foot and he becomes Paymaster on 12th August 1862;
Something wrong there. 105th Foot was previously the 2nd Madras Light Infantry.
I suspect the actual sequence was that when the 5th Bengal Light Cavalry were disbanded in May 1857, due to questions about the loyalty of the Indian soldiers during the Mutiny, the newly appointed Lt Davidson transferred to Madras Light Infantry, since the European officers were on contract. And as he was now probably a quartermaster his riding skills were less important than his organisational/administrative skills, hence his later appointment as paymaster.
Going back to mweston's original posting, it would be really helpful to find his records at the time when he later went on half-pay as they might include more details about where he was living etc, which in turn might throw more light on his origins.
I also think the word 'gent' in the Gazette entry Shaun linked to is helpful. It it may indicate something about his origins, although I think it just a standard way of referring to someone didn't previously hold a commission in HM Forces. In other words this was the date on which he formally joined the British Army.
