To approach it from a different angle, where was your grandfather from and when was he born?
Looking at the newspapers (1910 - 1919), two military Robert Eglintons appear.
Stirling Observer, 17-11-1914 - A list of men associated with the Erskine Church in Stirling who are serving etc. : includes Robert Eglinton, address Married Quarters, A.P.C. (Army Pay Corps?)
There is also a Robert Eglinton, alias Thomas Robert Eglinton, alias Thomas Bradley, who was serving in a "Scottish regiment" and was convicted of theft at Luton, Torquay and Paignton. The Police Gazette reports him being charged again for "improperly wearing military uniform". According to the report (1-5-1917) he was aged 27, a labourer or soldier, and a native of London.