I checked the 1911 Census and there was no reference to John during that Census year in England or Wales. Eliza has written that she was "Deserted Wife" and the enumerator has crossed that out and entered "Married".
Eliza died in 1927 aged 59 years Reg District Burton T. Vol 6b Page 361 as mentioned at freebmd.org.uk site.
Her probate (found at probatesearch.service.gov.uk) doesn't mention her husband so he possibly never returned to the family.
Over Eliza Letitia Hope of 171c Horninglow-street Burton-on-Trent died 19 May 1927 Administration (with Will) Lichfield 9 July to Jesse James Over army pensioner and John Henry Hove Over lasting operator. Effects 1109 pounds 17s. 3d.
The wording from the above would suggest that Jesse and John are two of Eliza's sons born 1897 and 1901.
I checked for a possible second marriage for John, but couldn't find any likely suspects. Sadly it is possible that he may have left the UK or changed his name.