A/C Blower (fan) will not turn off

A/C Blower (fan) will not turn off, even with car off and key out. Other than that, the A/C appears to work correctly. Blows cold air and flaps open and close.

rockauto. Com shows a "blower motor control module" - a small box with one three-wire and one four-wire connection. I cannot find a box like that anywhere, but I believe that to be the "power-train control module" that only controls the engine cooling fans.

I do find a larger box (passenger side under dash right side), with one 24-pin connector and one 32-pin connector labeled Delco 16231496 which apparently is a "programmer, A/C electric temperature and motor control".
I replaced the 16231496 with another one - fan would still not turn off.
I removed both connectors from the 16231496, reconnected the battery, and the fan still comes on - ignition off and key out.

In the Chilton wiring diagram, I see only three connections to the blower fan - an always hot, a ground, and a "blower speed control". Is the fan supposed to default to on (high) when there is no signal on the "blower speed control" wire? Or is the speed controller incorporated in the blower fan motor defective?

Could it be a stuck relay (I don't see one)? If so, where is that relay?

Am I mistaken and the "blower motor control module" that Rockauto and others list is actually involved with the blower fan motor? If so, where the heck is it?

Can the problem be anywhere but in the blower fan motor internal controller?
Can that internal fan controller be replaced, or is it necessary to replace the whole blower fan motor?