[cypress TX 72]

I can tell you this - that the ignition is no way connected directly to the blower motor - BUT - the fan switch is right next to the ignition switch - so I bet if you look under there I bet that the Ign swith is loose in the ring and when you turn the key counter-clock wise ( making the bottom turn the direction of the Fan Switch) to shut it off - it connects or bumps the switch just enough to make it come on for a second or two -
Id be willing to bet a loose wire at the fan switch or loose connection is causing the connection and is being caused by the turning of the key -
There is quite a few wires connected to that speed switch in a very little space. always a problem

There is absolutly nothing else it could be - at least not at that particular time.

shake those wires and see what happens!

Lucky this is a "NO MONEY" fix

Cypress