Do you have the occupations of any of the Rule men? Or any clues from the Parish Register entries whereabouts in Linlithgow they lived? Quite often, the entries in PRs will give the name of, say, the area, or even farm, (if they were farmers), of the residence of the father, and sometimes their occupation. I presume you have seen all the entries in the Linlithgow PRs?
This might give you clues to which children were born to which parents.
Scottish naming patterns might also give you clues to which children were born to which parents.
There is also a great site here
https://scotlandsplaces.gov.uk/It is not just about 'places', but about the people who lived in those places.
It has all sorts of taxes - Farm Horse Tax, Hearth Tax, Cart tax, Land Tax - about 15 different taxes ranging from the mid 1600s to about 1800, and how much each person paid.
Here is an entry in the Land Tax records for a James Rule in Linlithgow 'paroch' (parish) in 1667.
https://scotlandsplaces.gov.uk/digital-volumes/historical-tax-rolls/land-tax-rolls-1645-1831/land-tax-rolls-west-lothian-volume-01/1Luckily a lot of the original images have been transcribed - scroll down to the bottom of the page under the image.
I note there is an 'Allan' Rule just two names above James.
Might be the same family.
Another one for a James Rule in the Land Tax in 1771 in Linlithgow.
https://scotlandsplaces.gov.uk/digital-volumes/historical-tax-rolls/land-tax-rolls-1645-1831/land-tax-rolls-west-lothian-volume-02/2This one is not transcribed, but is not too difficult to find him.
There is also a wealth of other information on the site.
Make sure you have some time to spare if you start searching it!
