We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
It's more than that. If you are raised in a multi-child family your position with your siblings "can" determine which role you choose. As can a dominant parent(s) and/or a lack of love and respect from the parents. Then, throw in mental health issues and learned/intuitive responses and the possibilities are endless.
I prefer to think of them as sheep, guard dogs and wolves. The difference being in my version the guard dogs are always motivated by "doing good" where as in the Karpman Drama Triangle, the "rescuers" motives can be attributed to being a victim seeking revenge OR being an oppressor seeking power. In fact I suspect some combination of those two views is probably more correct.
I would separate the drama triangle from your sheepdog analogy because each position on the triangle is defined by dysfunction. The roles are to immobilize and gain power over others. The way to win is to not play. Get off the triangle, leave the drama.
Remember: the victim position is the most powerful in this triangle. If I react by persecuting or rescuing then I strengthen the victim. The way out is to do neither, to act as an adult rather than as the child who acts as one of three.