As you probably already know it is highly unlikely a deer or elk would attack, but in the one in a million chance one would (has happened I know). Then Bear spray or mace which is an irritant would just as likely cause them discomfort and to disengage an attack as it would a bear or person that was attacking. Nother words I don't think they'd like it.
Did Trigger attack and you had to use your bear spray? Sorry, I couldn't resist. I would think it would work on deer or elk but who really knows. As mentioned before, it is an irritant and should effect any animal.
I work with horses for a living and it will and does effect horses . It will not necessarily effect their skin but if sprayed in their face wear it is hitting more sensitive like the membranes around the eyes mouth or nostrils it would work. A few years ago in yellowstone a ranger was attacked by a cow elk around Mommouth springs . She had a calf with her and she charged him and knocked him off his bike. He turned his bear defense on it and it turned the cow away .
What does "gauge" mean anyway? As used here gauge means the number of round lead balls the same diameter as the inside of the barrel (aka the bore) that it would take to weigh one pound. It takes 12 lead balls the same diameter as a 12 gauge barrel to weigh a pound. The smaller 20 gauge would require 20 balls of that barrel diameter. The larger bore 12 gauge would require 12 lead balls of the bore diameter to weigh one pound.
In general the number of pellets in a shotgun shell...