The gauge you need is sold in the NSRA shop and is listed as the 0.22A. it has a slower taper than a 0.22 plug gauge so when pushed gently into the .177 shot hole it will centre itself properly to enable reading of the .22 oversize scoring ring when it touches the target.
The NSRA scoring course suggests the use of the plug gauge you have pictured with the wobbly spring on top can actually distort the score reading as light distorts when passing through the magnifying glass.
Regards Neil