I like the idea of engaging the child. Maybe he is playing a game that would amuse both of them, or OP could suggest that, though this seems rather rude to Aunt. However, once she got to know him, OP might find she actually enjoys his company.
OP is not a stranger. She is adult family. That brings this, for me, into a gray area where the normal host/guest rules may not apply. In MY family that would give her standing to tell a kid to get lost for a bit, when appropriate, and she would also have standing to say, "let's go in the (other room)" unless this room is the only place Aunt has to receive visitors, and she then she could suggest going out.
Visiting when the child is in school seems the most obvious choice.
As a child, I, as well as my children, were told to get lost (go outside, ride bikes, shoot baskets, go do something in another room, etc.) by parents, grandparents, aunts, uncles, and relatives of varying lesser degrees lumped together as Aunts and Uncles (adults) or Cousins (closer to one's own age). We have strong boundaries between adults and children, though those change and become flexible and individual during the transition years. Only OP knows what norms apply in her family, but I don't think it is as cut and dried as some PP are making it out to be.