Installed a new toilet (AS Cadet 3 from HD...and yes I had to take it back twice due to defects) that is a 10 inch rough-in into a 12 inch roughed in space. This was done b/c the wife didn't want a ADS/right height/tall toilet and the only short ones HD had were 10 inch rough-in. Everything seems to work fine but there is a pretty big gap between the tank and the wall, maybe 5 inches or so.

I'm curious if it would be a smart idea to brace the tank to keep it from leaning back should someone (like the cats) bump it just to keep it from moving?

Also, in the other bathroom (for a 13 year old kid) would it be wise to do the same there? That toilet is a 12 inch rough-in toilet in a 12 inch roughed in space so the gap is only an inch or two.