The AI seems to work best when given command at the theatre level. I tried giving commands at the Army level and the AI decided to do a little sitzkrieg with Poland. Only when I restarted and directly told OKW to go take Poland did it actually start attacking.
Later, I decided to detach 4th Armee and have it go beat up Denmark while OKW prepared to blitz through the Benelux. 4th Armee prepared for the offensive nicely, though one division got left in Poland for some reason without orders. OKW interpreted 'prepare to attack the Benelux' as 'guard the Soviet Border'. When given Blitz command and objectives of Kolding and Copenhagen 4th Armee advanced into Sonderberg. . . and stopped there. I declared war on Denmark 15 November. I got it to advance more by giving it more objectives like the airbase at Aalborg. Denmark was still there at the end of the scenario, as I wasn't going to ruin my AI test by manually controlling them. Oddly enough, OB West had sent divisions up that were taking as much ground as 4th Armee. OB West had no objectives set, only Defensive Stance on the Western Front.