Digital controls are discussed in this post:
The AC Delco number 15-72813 you found is for the REAR blower speed control on EXT/XL models (long wheelbase). Not for you.
GM 89018778 is a good part number for the item you need. You can also take yours out and look at it for a label, since you might find the issue is overheated wiring connectors, not the module itself. Take a look before you buy anything. If wiggling the connector makes it work intermittently, you need to clean that up or also buy a connector pigtail.
What you really need from rockauto.com or Ebay or the aftermarket stores is ACDelco: 15-80567
Oh, BTW - I can't claim any sort of godhood - I'm merely the Oracle.