I did a little more poking around the internet and found these emblem or badge backing plates:
Not exactly like yours, but I think you can see what I'm talking about...
Also found other info referring to backing plates for helmet/hat/shako badges:
________
Issued from 1881 to 1914, the Helmet Plate Centre replaced the earlier 'numbered' glengarry badges, which, following the Cardwell Reforms of 1881 gave regional titles to regiments. The Helmet Plate Centre (or HPC as it is normally referred to) could be worn either on the glengarry (when it would be worn with a detachable crown set above it) as the undress cap, or alternatively the Helmet Plate Centre could be affixed to a large
universal pattern brass plate when it would be worn with the infantry helmet.
AND
The two (sometimes three) loops pass through either the material of the cap, or
the holes in the backplate, once through the cotter pin secures the badge in place.
_________
The large hole in the centre would accommodate the regimental title badge.
So... I still think it's a backplate for an emblem or something similar.
I tried thinking about it being an electrical connector, but I can't come up with any reason why a turn-of-the-century rifle range would need electircity or electrical devices.
DCMatt
(OK, I think I have too much time on my hands at the office this week...

)