There is a clip on you-tube that has a few seconds of Ray Abshire at a festival. It only shows his left side.
It looks to me like he is holding the bass note button down and pumping the bass cord. At one point he seems to bump the bass cords without the bass note.
Unfortunately, the clip only lasts a few seconds then cuts to other players so it is hard to study.
It lead me to wonder what methods others use. I would expect there is a lot of "feels right", in people's playing.
I took an accordion class at Augusta from John Vidrine. When he wasn't helping us newbies, he would play for us, and his left hand playing was remarkable, lots more variety and style then just alternating. OK, all his playing was remarkable, but we're talking left hand here. And thanks for the tip.