I have found a bit of information that changes my earlier assumptions about T Battery RHA, 14th Brigade service locations in the Middle East.
I have found details of five T Battery Royal Horse Artillery dead. All are on the Western Front with a range of dates from 1916-1918:
Miller, Herbert Brown. Gunner. T Battery RHA.14th Brigade. Died 16 APR 1917. Buried Point-du-Jour Military Cemetery France.
Brown, Alec Charles. Driver. T Battery RHA. 14th Brigade. Died in action 22 AUG 1918. France & Flanders. Buried in Besles New Military Cemetery, Calais.
Stammers, Robert. Driver. T Battery 14th Brigade RHA. Died 27 DEC 1916. Buried at Mont Houn Militiary Cemetey, Le Treport.
Knox, Charles. Gunner. T Battery RHA & RFA. 14th Brigade. Died in the Somme. 16 SEP 1916. Buried in Longueval, France.
Reynard, Ernest. T Battery RHA. 14th Brigade. Died 31 AUG 1916. Buried at Dantzig British Cemetery.
It appears that T Battery RHA, 14th Brigade started the war in August
1914 in Egypt and was later transferred to the Western Front.
There it saw service with 7th Division. It was involved in engagements
at Neuve Chappelle, Loos, Guillemont, Bullecourt and many others.
I am still looking for more information.