Hi Totally Leics!
It's worth remembering that there may be people in the Hallaton and Medbourne registers who do not appear in IGI - hence the need to check.
But it does look as if William who married E. Brewster must be William 1771, son of Thomas Gibbins and Jane Freestone. They also have John (1767) and Amelia (1769). I expect you have seen that there are two other Medbourne Thomas-Jane marriages round about then, one with children William Jane and John (1749, 52, 55) and another later, with children Thomas 1779, Robert 1782, George 1785 and Francis 1790. It seems unlikely that all three father Thomases are the same, having children between 1749 and 1790, but there's a fair possibility that the second and third ones (ie yours and the later one) are the same father Thomas, maybe with two wives causing that gap from 1771-1779. Then the span would be 1767-1790, perfectly possible. All these seem to have nothing to do with Thomas and Elizabeth, who have a family of eight at Hallaton between 1755 and 1772.
So it's a good theory that your Thomas is Thomas son of Thomas and Sarah Carter, 1747 of Hallaton, though he would also be the prime candidate for the Medbourne 1779-1790 family, so the possibility of two marriages remains. Or maybe one marriage with a long gap with no record of children.
It must be right to rule out the two earlier Hallaton Thomas-Jane marriages, namely Thomas=Jane Patmon (Marie and John, 1730-1731) and Thos=Jane Bond (John 1738, Elizabeth 1740, Henry 1742) as possible fathers for your Thomas. Of course they might have had children called Thomas, but IGI doesn't tell us.
For your elder Thomas, (who married Sarah Carter) - we haven't got that marriage, have we? - you might cautiously consider Thomas (bp 19 June 1713), the fifth of six children of Henry Gibbins (GIBBENS) of Blaston - they were Sarah (1707), William (1708), Henry (1709), Ann (1711), Thomas, and Elizabeth (1714).
I count that William Gibbins and Eliz Brewster have 7 children (1800-1813), Henry being the eldest surviving son (Thomas 1800 died in infancy). Thomas and Sarah (Carter) have six, 1747-1758, including a infant mortality Edward of 1754 'replaced' 1758. Lots of room there for lateral investigation.
I think it's possible that my Henry Gibbins, father of Lydia and Elizabeth (Medbourne), is Henry 5th April 1751, 3rd son of Thomas and Sarah, brother of your putative ancestor Thomas, who is the elder. But then he might also be Henry 1752, son of Henry & Elizabeth Sewell of Blaston, in which case his father Henry is probably Henry 1709 son of Henry the elder of Blaston. Or even (though I doubt it) he might be Henry the son of Thomas Gibbins and Jane Bond (10 June 1742, Hallaton) - so I am really up the creek! About now a will or two would help.
Like space-spaghetti, isn't it?
Mercian