Mike,

it's the Ancient Hunting McIntosh tartan backing.

There were differences between the 2 Battalions during the war as far as their insignia are concerned. The only regimental distinctions worn by the 2FFY were the cap badge with the Ancient Hunting McIntosh tartan backing and the regimental arm flashes. Officers in the 2FFY did wear silver collar badges on their OSD however. Collar badges and brass shoulder titles were only worn on battledress by the 1FFY.

Concerning 1FFY, here is description given by Eric Annable who was in that regiment: Being in the 1st Fife & Forfar Yeomanry Tank Regiment our uniform was the same as everyone elses but with a few embellishments.

Khaki battledress comprising of khaki trousers and blouse, I had a belt for my waist as it was home to my weapon which was a revolver. The belt was actually optional in our squadron. The driver and co driver had a sten gun (small machine gun) which was quite dangerous because if you dropped or banged it accidentally it would fire a round of ammunition. There were a few near misses! The radio operator who was also the gun loader also had a Sten gun.
On our heads we wore a black beret, this originated from the first world war when the French gave the Royal Tank Regiment the honour of wearing their black beret.

Towards the end of the war whilst we were in Germany, we stayed at Geillenkirken. On arriving at the town, a unit of the Guards, (I don't know which regiment) saw the regimental badges on our shoulders and assumed that we were officers, they walked by and saluted us. We of course saluted back. It was a short while after when they got closer they realised that we were the same as them!

Our berets, collar badges and shoulder badges also had an adverse reaction from the native German people as they were very similar to a German SS Regiment who had treated their own people very badly. On entering the town, the German people gave us a very wide berth.

Hope it helps.
Cheers
Phil