The rule for the end-effects on this one is surprisingly simple:
"If nobody gives you their hand, don't go anywhere."
The messiness usually comes from people feeling like they should be going somewhere, similar to what happens with a diagonal chain or right & left through. This is just different enough that people don't think to stay put if there's nobody there.
The end result is that as you're going off the end and back in that:
pull-by-left: everyone moves
pull-by-right: gent stays put
pull-by-left: pull by with partner
pull-by-right: lady stays put
If you have an odd number of couples, there will be a couple out at the end which gives you a slightly different sequence, but in principle it's the same.