Roy Page FRES who must now be well into his nineties told me that in his
teaching days one of his students ( I guess in the 50s) noticed a shaking
dance such as Aaron describes.  From the reactions of other bees the message
was "I have this itch between my shoulder blades where I can't reach.  Can
you scratch it for me please?"  ie an invitation to groom.

This was in the UK decades before varroa appeared here.

Chris