Thanks for the help, zompist. I've done some searches using the terms you gave me, and found a few things. But the problem is, verbs still have to fall into one category or the other, and I'm no closer to finding out how languages divide them. Even if a language has no ambitransitive verbs at all, it still has to divide them. Let's say every verb is marked for transitivity, or even has a separate root for every transitive and intransitive verb. Even then, a verb has to lexically determine whether the subject is an agent or a patient. If you have a transitive Japanese verb like "mashiru" and the intransitive version is "mashikeru," you still have to assign Mashikeru an agentive or patientive role. I've made charts of lexical aspect, trying to see if telicity, duration, dynamic vs stative properties, cumulative reference, and a plethora of other features, match up with whether an intransitive subject is an agent or a patient. And so far, I have found no pattern whatsoever in English, and I haven't found any pattern in Korean, Russian, and Japanese, but these languages I don't know so well, and some of them have weird aspectual affixes that complicate things quite a lot (like Russian po-). So I still don't know what makes a verb fall into one of the two categories I listed above, other than sheer random assignment.
Japanese is the only non-English language I can give you information about, but here goes:
Basically, in Japanese, the subject of an intransitive verb that has a transitive counterpart is, as far as I can tell, always the patient/theme of the transitive verb:
誰かが鞄を落とした。 - Dareka-ga kaban-o otoshita.
- someone-SBJ bag-OBJ dropped.TR - Someone dropped the bag.
鞄が落ちた。 - Kaban-ga ochita.
- bag-SBJ dropped.(INTR) - The bag fell.
肉を焼いた。 - Niku-o yaita.
- meat-OBJ cooked.(TR) - (Someone) cooked the meat.
肉が焼けた。 - Niku-ga yaketa.
- meat-SBJ cooked.INTR - The meat cooked.
大震災が私を変えた。 - Daishinsai-ga watashi-o kaeta.
- disaster-SBJ 1-OBJ changed.(TR) - The disaster changed me.
大震災後、私が変わった。 - Daishinsaigo, watashi-ga kawatta.
- disaster.after, 1-SBJ changed.INTR - I changed after the disaster.
It seems that in any case where in English where an intransitive verb has the same subject as its transitive counterpart, in Japanese the verb simply remains transitive but leaves out the object.
私が肉を食べた。 - Watashi-ga niku-o tabeta.
- 1-SBJ meat-OBJ ate.(TR) - I ate (some) meat.
私が食べた。 - Watashi-ga tabeta.
- 1-SBJ ate.TR - I ate.
If I can think of any exceptions I'll let you know.