Connection Failed error message with PeopleTools Change Assistant on 64 Bit Windows

With PeopleTools 8.5, Oracle moved the app servers into 64-bit territory. That was welcome news. Unfortunately, the whole stack isn't quite there, yet, and we ran into an irritating problem when running Change Assistant to upgrade from 8.49 to 8.51. Specifically, when setting up the environment, we recevied a "connection failed!" error when testing the connection. Here's what we saw: No logs, no details. Just failed. But then, finally, a hint: Data mover (which shouldn't connect, since the database is still at 8.49) wouldn't even run: it failed with an error "missing or invalid version of sql library psora". Aha! Now that is something one can work with. It turns out it needs the 32-bit Oracle client. Install that, and everything is good, again.