Are all healthy animals more likely to defecate near the end of a rest-cycle?
I think we can actually go farther than mere behavioral argumentation. The separation of the autonomous nervous system into parasympathetic and sympathetic is, one the one hand, associated with the sleep/wake cycle, on the other with parasympathetic/sympathetic activity (low/high epinephrine secretion). This duality certainly applies to all vertebrata (i.e. big animals), as fight &amp; flight is associated with all vertebrata, see e.g.

http://en.wikipedia.org/wiki/Fight_or_flight_response

In other words: from the existence of fight or flight in all vertebrata I infer the existence of a dual autonomous nervous system (parasympathetic and sympathetic) in all vertebrata, although there may be other proof. Since in sleep the parasym. NS is active, the bowel moves. Conclusion: the bowel moves in the sleep of all vertebrata.