Is comma needed and meaning of 'wavering'

waver - hesitate, pause or hold back in uncertainty or unwillingness, falter, be unsure or weak

The line is from the short story by Anita Desai, "Private Tuition By Mr Bose." The latter was beginning, uncertainly, to smile. If Ms Desai, a competent and knowledgeable writer, thought that a comma was needed, she would certainly have inserted one.