Help with mystery Scottish Tartan PTI Badge?

[biffrocks]

Hi Guys
I picked up this badge this morning and am I right in assuming it's a PTI badge and am wondering if anyone can help with the Tartan backing and what uniform it may have been worn on with the red backing.
There a 3 holes in the badge and is there something missing or was this how it was attached.
Also am I right in it being a Kings Crown and there for pre 1952.
Any help or advice very much welcome.

Thanks

Rob