Can't help re a grave picture, but to keep this thread active until someone possibly sees it who can, thought we might add some possibilities for family members.
CWGC look to have added William to their 'appeal for relatives' list in September 2021. Haven't seen any search here on Rootschat for them, as is sometimes done. Don't know if they found anyone.
Anyhow, St George's is mentioned earlier in thread, as was a sister, Catherine. So, these two births seem promising:
PIRIE
WILLIAM ALEXAND
LIVINGSTONE [mmn]
M
1905
644 / 9 / 104
KELVIN
and
PIRIE
CATHERINE LIVIN[STONE]
LIVINGSTONE [mmn]
F
1899
644 / 9 / 987
KELVIN
Potential for parents being:
PIRIE
WILLIAM WHITTET
LIVINGSTONE
MARY ANN
1895
644 / 8 / 276
MILTON
Middle name for above Catherine fits well with initial in the the Catherine L Pirie marriage to Joseph Gibson.
Her death, cross indexed under Pirie:
GIBSON
CATHERINE L
72
F
1971
644 / 9 / 1013
GLASGOW
If potential parents correct, then death of William's mum would seem to be:
PIRIE
MARY ANN
43
LIVINGSTONE [mn]
F
1914
644 / 13 / 603
KELVIN
and his father's death, again if correct parents:
PIRIE
WILLIAM WHITTET
74
M
1943
644 / 4 / 960
PROVAN
an infant son of same name as above was also born/died in 1901 in Kelvin district.
No other siblings obvious. edit to add this possible birth:
PIRIE
FRANCIS GARDEN
M
1896
644 / 9 / 1547
KELVIN
There seem to be about five or so possible births to the Gibson/Pirie marriage, but as after 1919, and some could still be alive, I won't list them here. Some were infant deaths.
A Margaret Shanks Gibson nee Smith died aged 45 in Helensburgh area in 1984, and may have been wife of one of the Gibson/Pirie children. Not seeing an obvious death for her husband, who may therefore still be living.