During a battle (on the excellent Waterloo map) using a couple of small random OOBs, I noticed an enemy regiment had moved far ahead of its Corps and was behind my lines. I sent a cavalry regiment (out of a Corps of 8 regiments) to harass it. The regiment moved up to about 500m away and stopped. And waited. I ordered in two more, putting one in support and ordering the second to attack. They took up positions...and waited. The attached picture square1.jpg shows the viewpoint from the infantry square.
After a long time I got bored waiting and so I ordered the rest of my cavalry Corps up to attack the square. Each regiment dutifully took up position - square2.jpg - and waited.
After another hour or so of game time, I ordered the Corps off. Three regiments obeyed, four continued to watch the infantry square.
At no time did the infantry have any support but they remained calmly in square , in sight of at least twice as many cavalry and entirely surrounded.
I'm not sure how to interpet this. I was fighting with the default doctrines in conscript mode. I suppose I should have brought in some horse artillery to blast the square but earlier in the same battle when I ordered one battery to unlimber at a particular place I had chosen, it continued to advance toward the enemy and got itself destroyed.
I think there are still questions about the AI. I would like to see more feedback about why units do not obey orders, even if only in a log made available after the battle ends.