it doesnt bother me it being an elephant but to answer your question...
gai's technique seem to represent the 4 celestial guardians of the compass..
morning peacock - the vermillion bird southern suzaku - element fire.. morning peacock looks like fireballs
Afternoon tiger - the white tiger western byako - element wind.. hirudora is a compressed blast of air
gais summoning is a turtle - the black tortoise northern genbu - element water
so from this itself i assumed it was following the myth .. the last guardian is..
the blue dragon Eastern seiryu - element lightning (wood)
so i was sort of expecting a lightning look dragon taijutsu tech