I suppose there are 2 reasons why you might want to look at Margaret & Eliza Booths deaths and that’s in the hope that one might be George’s senior’s wife. It may say “widow of George Booth, farmer” for example, or the informant might be a relative you can identify from other records. The second reason is that all the Booth families in that townland were probably related somehow and so if you can identify them all, then it’s sometimes possible to build up a bigger picture of who was who.
But getting back another generation may not be easy. Whatever denomination John was at birth, there’s only 1 church in the area with baptisms for 1820. The Presbyterian records don’t start till 1848 & RC till 1827. Only the Church of Ireland has records from 1775 onwards, and they have some gaps. So unless John was Church of Ireland, there’s not much chance of finding firm records showing his parents. If George junior was the first born then that’s a slight clue. The Irish (and Scottish) naming pattern was to name the first son after the father’s father. And we know there is a George senior of the right age whose farm passed to John. However the couple appear to have married in 1845 and so George in 1854 doesn’t seem likely to be the first born son. Not every family followed the naming pattern of course.
Arboe Church of Ireland records are not on-line anywhere so far as I am aware. There is a copy in PRONI in Belfast but a personal visit is required to search them.
I did find this link which records John’s death in 1912. The records appear to show that his father might have been George (There’s a question mark beside it).
https://cotyroneireland.com/churchrecord/arboe-rc2.html
I also noted a possible brother to John Booth. There’s a George Booth b c 1820 s/o George who married Susan Mooney. He’s noted as non Catholic which fits with your speculation that John wasn’t born Catholic either. Incidentally if they weren’t born RC, then there would normally be an adult baptism to convert them. Often about 1 or 2 months before the marriage. Have you checked the Arboe RC baptism records for that? Adult baptisms usually stand out because there are not normally any sponsors.
I haven’t searched the Co Tyrone genealogy site thoroughly. You might want to do that to see if you can find any other references to your family.
I agree that to be sponsors at an RC baptism, they have to be RC but there’s not much more you can infer. They might be relatives, but they might not and there’s no way of saying what the relationship was.
There seems to be some sort of connection between the Elagh Booths and Kilmenagh Booths. I see an advert in the Mid Ulster Mail 23.2.1918 where James Booth of Elagh is selling land in Kilmenagh in 3 separate lots.
The Tyrone Constitution of 10.9.1886 mentions that John Booth of Kilmenagh had his entitlement to vote challenged at a local electoral court. However when the case came to be called forward it was abandoned. (This was at a time before there was a universal vote and your right to vote was linked to how much land you had and also, as is still the case today, whether you actually lived there. At a time when Irish nationalism was on the rise, every vote counted so people were quick to challenge if they thought someone was on the voters list who shouldn’t be there. The papers are full of cases where the registered voter was actually in Scotland or even Australia, but was still on the electoral register in Ireland. If there was an election someone else would often impersonate the registered voter. We finally brought in a requirement to produce identification in elections in Northern Ireland about 20 years ago, at which point 10% of the names on the electoral register vanished. That tells you how mush impersonation was going on!). I can’t tell you what the reason for the challenge was in the 1886 case because obviously it was abandoned before it came to court.
Most Irish research comes to a stop around 1800. The lack of earlier records usually means there isn’t anything left to look up. There are exceptions for folk who were very wealthy, big landowners etc, or infamous, but for the average man there are almost no records left to research. And even fewer for the average woman.