Portrait of an unidentified young woman with curly hair upswept hair, London, Ontario

Here the word Sunbeam probably means both the production process as well as the posing.

The fact that it is on the front of the card puts it into the realm of advertising by the photographer to distinguish himself from the competition.

This taken from the internet

"For the production of negative pictures, the ordinary illumination is not sufficient, and recourse must be had to the sunbeam, which should be reflected upon the object by the plane mirror when powers are used not exceeding the quarter of an inch combination. It is not necessary here (when producing negatives by the sunbeam) to allow for the 'over-correction' of the object-glass, but merely to focus the object carefully upon the ground-glass plate.

"In the production of negative pictures, a moment's exposure to the sunbeam is sufficient when using the lowest powers, and with the highest I have varied the time from five to ten seconds."

Perhaps Bob Lansdale can shed some more light on the subject(no pun intended) when he next visits the London Room.

Thanks, again, for this. Another possibility is "Sunbeam" is a nickname given to the model or her 'look' in an effort to make the photo a collector's item, something like a modern hockey card.