No i´m afraid i don´t, i am only going by his WW1 Records saying he served in both Army Units, i was under the understanding that the Cycle Reg was retired in about 1916 ? not that i have found out much about the unit or where they served.
Of couse poc could of been taken anywhere in the U.K not saying he was home on leave or other person were from Birmingham, no it´s a long shot