I see Margaret in 1851, I believe - with her son John?
If she was a widow then, it narrows down the time frame for when John died.
1851: West Meadow Head, New Monkland, Lanarkshire
Head: Margaret WILLIAMSON 68, b Broxburn, Linlithgow
Son: John BOAG 45, Labour Cool Pit, b Broxburn, Linlithgow
Cheers
AMBLY