Very tame birds like playing a sort of tag, chasing you round the room, or dancing together games (either bird on cage moving with you, or you with bird on finger). Games are an important part of training and taming. Calling to the bird when you enter the house, and seeing if it responds. Calling to the bird before feeding, so it knows what to expect. Calling to it before exercise time. Very tame birds will play with toys with you on the floor or at the table. Some enjoy watching as you wash dishes or vegetables (not while cooking!) and join in. My mother's hen budgie would spend hours placing tiny items like coat buttons or pieces of cardboard into a sort of circular pattern on the table.
