It seems that the naturally generated Ilex shrines will not allow you to use a gs ball on them, only those that are manually placed will allow you to use one on it.

After spending another 15 minutes warping around and checking out the biomes the shrines spawn in, it seems not even the beast balls will work on naturally generated Ilex shrines and they will only work on those that are manually placed.

On top of all this i hope it's a mechanic of the shrine to prevent mass spam of celebi's, but if you use a gs ball on one that's been placed you can't use another gs ball nor can you use a beast ball, and vis vera, you can't use another beast ball on it and you can't use a gs ball aswell.