OK, so we've had these dogs for about 5 years...
My wife found them when she was out walking our big dog. Someone had dumped them. The vet said they were about 6 weeks old at the time, just old enough to get their shots.
Ever since we got them they have done this weird thing: They will sit down next to each other, assume practically the same position, and hold it for about 5 minutes like they've gone into a trance or something. They aren't looking at anything (as far as I can tell). They can even be in different parts of the house; one will go find the other, and they will exhibit this behavior. At the end of about 5 minutes they will turn their heads, look at each other, and then go about whatever it was they were doing prior to the behavior (sitting on my lap in this case). It can be kind of unnerving. I've started wondering if they are downloading instructions from a mother ship somewhere... .
Seriously, anyone know anything about this type of behavior in dogs?
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It breaks my heart. 
Interesting about the pooping.
...sometimes, at least. 
I haven't noticed anything in particular that they do afterward, but I also haven't paid attention to it.
They often do this:
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But that is pretty much their default position much of the time.
These are brother and sister as well, we think. Here is how they looked when we first found them:
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They were magnificent creatures, and beautiful. I referred to them as their Royal Dognesses. Very closely bonded before we found them one day on the side of the interstate, abandoned, at about 6 months of age the vet said.
They were like 1 dog with 8 legs. They would lay or sit like bookends butt to butt or mirroring one another. They also were hunters to some extent and worked together as a team. One would distract the prey (or enemy/intruder) while the other circled around back of it/him. Very cunning.
They also had a very annoying habit that I nonetheless marveled at. They were basically outdoor dogs, but on occasion I needed to round them up for one reason or another. But if they weren't interested, they'd look at one another (as I was calling them), apparently reach silent agreement and then both bolt simultaneously and run away as fast as they could. (We lived in the country.)
They'd been abused as pups (most abandoned dogs are), so training them was tricky, especially for someone like me who didn't really know what I was doing. They were also a little headstrong and, as I said, deeply bonded to one another.
They were beautiful, wonderful dogs who never really caused us any trouble but, as pretty much all dogs do, gave us a lot of joy. We had them 15 great years and I miss them.
They can be real bed hogs as well.
They looked exactly alike at 6 weeks, when we found them. Mordie went on to develop the Chorkie characteristics, while Hildie proved to be full Chihuahua (or so it seems).
There hasn't been any problem with bonding.
Every pet we've ever had has been a rescue, including that cockatiel in the background. 
They never appear to be in any distress and they will snap out of it if I call their names, although it usually takes 3 or 4 times. They don't seem in ill health in any way. Animals do get seizures.
It's the world of animals.
They are absolutely adorable.Sorry, I know nothing about dogs, cat woman here, but they are awesome! I guess you just gotta go with the flow with their little quirks. My cat, Otis, can be laying on the floor, blissed out in a zen-like state when all of a sudden he'll wake up then run over to me & look over my shoulder in horror. There's never anything there, but talk about unnerving... 
