is the north and south nod just a slow up and down movement?

I'm not quite sure either, Wordwind. But I think it's not so much the character of the nod itself [altho it's probably shallow - figuratively and literally - as well as slow and phlegmatic] but the fact that it is not accompanied by any words of encouragement, or by any follow-up action.

For me, the key to the "north and south nod" is in this bit:

You could go brief them, but you never saw any initiative come of them. You just kind of got a north and south nod.

The "north and south nod" is not a true nod of assent because it leaves the petitioner with the uneasy feeling that there is no conviction in the nod. Of course, the proof of that instinctive unease comes later when absolutely nothing happens to lend substance to the nod.

It reminds me of the expression "to damn with faint praise". The "north and south nod" damns with faint assent.

The "north and south nod" is the tell-tale sign of someone who is 'just going through the motions', in this particular case, by submitting to the ritual of the "briefing".

The nod can, in fact, serve as a polite signal that the "ritual" is over. The petitioner goes away harboring some hope that their argument was successful, and the nodder goes away without having actually said anything for which they can be held accountable later.