Wiggles Club Member x3.
It is adorable when they do this. It's like their bottoms are possessed of their own free will.

-A Blackmouth Cur that has her tail but her whole body all the way up to her head, including her ears, wiggles when she wags.

-A Vizsla/boxer mix, similar body type as yours. She has her tail though, skinny thing, but her bottom wiggles like a boxer and she almost arcs in half back and forth while her bottom wiggles with excitement. She reminds me of a wiggling noodle. She also has to bring me something in the process, some kind of treat or toy which she cannot always pick up or actually give to me because she is moving around too much but eventually she gets there and to hand it over.

-The third, an Australian shepherd/ lab mix that like an Aussie, her bottom goes in circles when she wags; she cannot walk either as her back end hops around up and down and around. If I didn't know better, I would think she was being shocked, it is so animated. It is a sight to behold.