You are probably thinking about shoe goo, not goo gone. You could remove the cover and shoe goo a patch over the tear from the back side.
However, the seat is torn because the vinyl has hardened with age. If you fix that tear, it will just tear on the other side, very soon most likely. cbjunkie is right, get a new cover for it. And, do it before the foam has a chance to deteriorate further which will happen much more rapidly now that there is no vinyl to protect it.
Cheers,