I have to say I was encouraged to allow my birds to be independent from the very beginning. I was told....teach them to play by themselves, and as hard as it may be, encourage "side by side" time together. So I have done what was suggested and my babies have no problem playing alone on a playstand or in their cage if I can't supervise. They enjoy their cage and I think as a result, they enjoy their time with me that much more!
I remember having a 2 year old that was always by my side....it can be frustrating! Hang in there, and be persistent!