Harry K wrote:

Waste the 'rock. You are talking about less than $10 (been a long
while since I bought any). It doesn't even have to be the full sheet.
Or just cut a good sized hole where you need it. Patching a big hole
isn't much more work than patching a small one.

Along those lines...if you use a keyhole saw and angled the handle
outwards, away from the hole, as you cut, the resulting piece will form
a plug for the hole. In other words you can smear some joint compound
on the edges put the cutout piece back in place and tape the edges. No
blocking or additional cutting needed and it doesn't matter what shape
you cut out.

R