So, when I was falling asleep, I started deconstructing the word. I've had a sort of a kink for making personal 'folk' etymologies since I was a kid.
Ambo + bi + valere
Both (of) two (that) are strong
It makes more sense now, in the contexts where it has confused me before. And while I was at it, I also convinced myself that 'amphitheater' came from ambo + phi (Φ) - both (sides of) the diameter of a circle, because I needed something to back up my ambo-theory.
I've had stranger ideas in the twilight. Like that the illusion of 'self' governing the combination of biology (feelings) and the sensory data we've amassed and stored from the 6th week after conception on (context) is merely an evolutionary trait that has guaranteed our procession as the dominant species of the planet.