I thought we got a major hint of it being from disrupting nerve transmission mechanisms. Due to of all things anesthesizing plants with gases resulting in disruption of "conscious" behavior like facing towards sunlight or venus flytraps closing upon being touched.
Oh yeah, there are several plausible theories with decent evidence to support them, but nothing remotely definitive.
Anesthesia is weird. I'm an anesthesiologist; believe me, there are tons of weird things about the human body that you learn from throwing various compounds at bodies and seeing what happens. Xenon is an effective (though expensive) anesthetic gas by itself. People of West African descent occasionally (~10-20%, usually on the lower end of that) have a hypersalivatory response to cholinergic stimulation. Drugs that should be fine and got approved but turn out to kill kids disproportionately (rapacuronium).
Much of our practice is derived from "we've been doing this without too many bad effects for a long time with these drugs, so we're going to continue using them rather than try something new unless the new one brings something to the table that's a slam-dunk". Diethyl ether is slow, it smells awful, and it's flammable (and will form explosive peroxides if stored too long), but it's still a good anesthetic. If I had to re-create civilization from scratch, that would be one of the first drugs I tried to make.
And a significant cardiac depressant, even by the standards of general anesthetics (which pretty much all have at least some cardiac depressant effect, even ketamine - you don't typically see drops in blood pressure because it stimulates the sympathetic nervous system, but if someone's been on an amphetamine binge and is out of catecholamines, ketamine will drop their pressure too).
In the days before routine pulse oximetry (which, in addition to measuring oxygenation of the blood, is proof of a pulse - it does not work on heart-lung bypass), the fact that the heart was beating was confirmed by using an esophageal or precordial stethoscope. This was typically connected to an earpiece that was molded to the individual user by a simple piece of tubing. Precordial stethoscopes are a neat thing to see; they are just the "bell" part of a stethoscope made out of a decent-sized piece of metal so that the weight would keep it on the patient's chest and prevent it from moving around. I'm told that anesthesiologists who practiced in this era, which was also before each anesthesia monitor had continuous gas sampling of the patient's respirations to determine the concentration of anesthetic agents, could recognize when a patient under halothane (which was also a well-known cardiac depressant, but unlike many other agents had a non-irritating smell and so could be used for pediatric cases without an existing IV, where anesthesia is induced by simply breathing the gas) was getting too deep by the change of the heart sounds. We have a newer, less cardiac-affecting anesthetic now, sevoflurane, which has essentially replaced halothane in developed countries and I would assume most less-developed ones as well (because it's now off-patent and pretty cheap).
