Hello Margaret - I think I
may have cracked your ancestor's military service - if so, he did serve in the Second Boer War as Private 765, 2nd Battalion of the Lancashire Fusiliers.
In Victorian times it was not uncommon for rank & file soldiers to enlist under a false name and often using their mother's maiden name. They were usually sussed out or even confessed to their lie when they realised their wife might not receive her due if the grim reaper came calling.
Assuming his mother was actually called Sarah Gallagher rather than Sarah Gollogher the following transpires:
He attested on 24th May 1884 and knocking 24 years and 2 months off gives a date of birth in early 1860 which does not quite conform to the DoB you give.
Page 4 of his service records gives the following details of his service:
This explains him being missing from the 1891 & 1901 Census returns. By the time he enlisted I believe his father was dead and giving his mother as next of kin using her maiden name rather than her married name was part of the subterfuge.
I found these service records on Find My Past and they also have attached medical records - if you send me a private message with your email address I will forward the complete set to you.
From a Public Family Tree on Ancestry I suspect you may have access to Ancestry. Afraid they do not have his service records but they do have the medal rolls for the 2nd Battalion, Lancashire Fusiliers. To find them enter "J Morrison" into a Military search and enter his service number "765" into the Keyword box. He should appear top of the list and twice - the two medal rolls show he was awarded the Queen's south Africa Medal with 5 clasps - "Cape Colony", "orange Free State", "Transvaal", "Laing's Nek" & "South Africa 1901".
Regards, David (Smethwick)