According to "The Thirteenth Hussars in the Great War" by Durand, the 13th handed in their steel helmets and drew "Cawnpore" piths immediately upon arrival in Mespot. Regimental flashes were affixed to these. This pic of Cpl. Vinall, DCM appears in the book.
https://www.britishempire.co.uk/forc...sarsvinall.htm
Other photos of officers and men suggest the flash was worn only on the left side and no other recognition signs were worn on the uniform or pith helmet. I couldn't find any mention of them in the text either. It's on project Gutenberg if you want to give closer reading.
https://www.gutenberg.org/files/6176...-h/61769-h.htm