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I will try to get a pic. It's were the shifter connects to the shift rod from tranny?
That's not a "ball".
If you meant to ask if the shifter itself will spin 360 degrees in it's ball & socket, yes it will IF the rod from the transmission is not attached. After all, the shifter handle / lever is mounted and pivots by a "ball and socket" type setup, remove the rod from the transmission linkage and it is free like "a ball in a socket".
Rotate it so longer side of attachment point is towards driver side. Bottom pic is a Hurst, but it illustrates just the same.