So, we have a new-to-us vehicle since the last time I posted (a 2015 Buick Lacrosse, these days), but that has resurfaced an old issue: our car's "universal remote control" (what other folks here seem to call HomeLink, but I'm not sure if that trade name applies to our vehicle) isn't able to learn how to work our garage door opener, a Craftsman 139.53966SRT (made by Chamberlain).
We have the OEM keyfob remote, which works fine; however, when we try to use either procedure in the car's manual for programming the car's remote, the light corresponding to the button we're trying to program simply blinks rapidly as soon as we start the process, which is a condition not even mentioned in the car's owner's manual. How can I go about troubleshooting this?