Turns out I already have a copy of the 1921 pension application, 1851 census substitute. I thought they had verified his pension but I see what you mean about not actually listing him. I also have the 1911 census which lists the two parents and William 1891 and John 1896.
Have you had a look at the 1901 Census for 8 Dunluce Street, Portrush, which has, James age 48, Maggie age 45, Maggie age 16, Mary age 20, William age 9, John age 5. No James (1879) and no Alexander (1888).
In 1901 there is also a John Fall, age 68, at 1 Dunluce Street, Portrush (Widower), and his son William, age 25, both born in Co Derry. Could be Margaret Rankin Fall's father? Living close beside his daughter as his wife was dead?