Many thanks for your quick replies and help. This is what I have interpreted from the information to hand which I have included here in case it is of any interest to anyone else on the Forum or anyone has any further clarity on his time in Birmingham. This information is part of a RBL War Graves Project for those buried in All Saint's Churchyard Birchington, Kent. A picture of his grave will be posted on Findagrave UK.
The first military casualties were brought to the 1st Birmingham War Hospital on the 30th July 1915
which had 1,100 beds. Robert Russell appears to have worked at the hospital throughout the war, though it is not clear from when. The hospital closed as a War Hospital on the 31st March 1919 having treated a total of 20,015 casualties. The 2nd Birmingham Hospital (formerly Hollymoor Asylum) which during the war had become a specialist Orthopaedic Hospital, closed a year later (1st March 1920) and became the Pensioner's Hospital, i.e a hospital for personnel officially retired from the military following the war. The majority of the patents would have been in the hospital prior to being "officially retired" and still recovering from their injuries, or transferred from other War Hospitals as they closed. The Pensioner's Hospital was kept open for a further two years and Dr HARPER as a medical superintendent, helped to take charge of the everyday running of the healthcare aspects of the hospital. It is likely that when the Pensioner’s Hospital was closed in 1922 and returned to being an asylum, Dr HARPER, now aged 68, retired to Westgate-on-Sea with his wife Marion. There is no obvious known connection with his choice of Westgate. He died shortly after, on the 4th of October 1924 there at 24 Adrian Square.