Mike,
Update - I'd lay a fair wager now that he was definitely 146RAC. Just been going back through some research I've been doing on RAC regiments and their cap badges and all three in 50 Ind TB wore the RAC cap badge - at various times through the war!
This was in line with the WO instruction that these war raised regiments had to wear the badge of the RAC and not their parent infantry badge. Machinations in the background went on with various COs and various regiments meaning that some succeeded in getting WO permission to wear their infantry badge. Just to muddy the waters completely some such regiments allowed the wear of both RAC and infantry badges within the regiment.
As to 50 Ind TB:
146RAC - RAC cap badge > mid 1944 (likely Sept as other two regiments?) then DWR cap badge. They also wore RAC shoulder titles so yours is almost certainly from then and not RAC training.
149RAC - RAC cap badge > approx Sept 44 then KOYLI cap badge.
150RAC - Y&L cap badge > late 1942 then RAC cap badge > approx 1944 then both RAC and Y&L in use.
John
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