Hi.

Here are the breakdown diagrams and 02-Controls parts for Maytag MSD2554ARW - AppliancePartsPros.com

Remove the cover #21 off and locate in the right rear corner the defrost timer shaft in the small opening.Use the flat screw driver to slowly turn the shaft CW for one full turn or until you'll hear the click.
If the fridge kicks on - replace the defrost timer #13

Part number: 68233-2

Update: I turned the defrost timer shaft, got the click, but nothing else.

Thermostat ordered. I'll post my results once it's installed.

Thanks again.

So apparently it took me 2.5 years to remember to post an update. Better late than never, right?

The replacement went well. It took me a few minutes longer than I expected to figure out exactly where it was living, and the replacement part was shaped a little different than the original (which took some tweaking), but it all went well enough, and it fixed the problem. My hero status at home went from 11 to 13, so thanks for that.

I've been meaning to get back in there and adjust the placement of the temp sensor, but I'm still able to get the temp I want via the control, so it'll likely stay as-is until it dies again.

Thanks again for the help; I hope this thread helps someone else with the same problem.