I cannot get him (or an acceptable alternative on ADRIC register) . There is a TF Wooley in Drivers & Vets for G Coy, and it is probably him - b14 Feb 1890, & a Motor Driver
This man worked pre-war as a "tester of cars for the London Omnibus Company"
1921 Nov. 26. Wounded at Corofin . Evidence was given by HR Gates . £281 compensation.