I keep several tarantulas and a few other spiders, and they are absolutely fascinating! Your description of the spider waving its arms and running from side to

I keep several tarantulas and a few other spiders, and they are absolutely fascinating! Your description of the spider waving its arms and running from side to side makes me think it was likely a jumping spider. This group of spiders have large eyes and don't build webs to catch prey, and are really cute!