Hello Kelly,
Look this really is not atomic science do you actually know who his mother was, well, perhaps not, but regardless, just start with what you know and then expand on it.
There are just so may variable factors here, you have a picture of a man who you have cause to believe is the man in question, he appears to be a rifleman, if he served in the Militia he may not have served for very long as men and boys joined, they might have served just a couple of weeks before being headhunted by the regular Army.
So a man might have joined the Essex Regt in the Militia and then joined the KRRC/RB etc, moreover, one way or another, almost everybody left a footprint.
You did not need a birth certificate to join the Militia or Army back then either, not like it is now, men often lied to get off the streets or for financial reasons, you could join as a boy, but, as far as money went, better to be a man, what I'm saying to you is that just because a man might have been born actually in 1878, it does not mean that the age on any service papers will suggest or tell you that, you need to look beyond the box sometimes, so you see looking at a James Vaughan born in 1878 as far as service papers go may well prove to be a mistake.
I see you are close to London, could not be better for you as far a this sort of thing goes, get yourself down to Kew, don't bother about reader tickets and the like, you won't need one for what you are looking to do, talk to people and look at what you already know for sure, that is beyond reasonable doubt.
You should look at WO96, WO97, WO363 and WO364 at every single J or indeed James Vaughan, but, before that start with the man himself and not the army.
This James Vaughan was born in 1878 in Surrey and his father was also James, you see where you can take this, often it is easier to prove a given individual is not who you are looking for than to prove that the same is!
Good luck Kelly.
Regards Frank