Just to add confusion to the topic. This ebay photo is titled the 13th Hussars and dated Jan 1923: so just after the 18th Sqn had joined the regt to form the 13/18 Hussars.
He is wearing the 13th Wreath collars, WW1 medal ribbons reinforcing my view that the 13H wore wreath badges up to amalgmation.
https://www.ebay.co.uk/itm/RPC-Postc...p2l:rk:93:pf:0
The second photo below shows the Z-type portrait dated to post WW1 by the cap style so should therefore date to post amalgamation but before the regt went overseas in 1929.
Speculation on my part but Tony's cap badge may well be a regtly procured badge hence the makers' name.