It may not always be necessary to uninstall the hardware drivers or plug or unplug the hardware or change axis assignments.
This morning I had the A/T blinking issue. I had read your note about the Honeycomb Bravo but don’t have that hardware. Using all Thrustmaster here.
BUT, out of desperation and frustration, I decided to try just the last two steps only; i.e. stick full forward to disengage the AP and then re-engage the AP. AND IT WORKED! After re-engaging the AP, I clicked the A/T button and it lit up solid.
God bless your efforts! If I hadn’t seen your note, I would still be tearing out the few remaining hairs I have left.