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There is no rhyme or reason.

There is *SOME* rhyme/reason because as you pointed out:

Iowa and Minnesota will always be on the Wisconsin schedule, so the other 7 games rotate.

I think that every team has a few that are always on the schedule.  

I don't know and don't care to look up all the ins and outs but most of the major rivalries will be played every year then each team will rotate through all the rest.  Also, I think the four western teams all play each other every year to minimize travel costs.  

I was wondering if everybody had perma-rivals the way the SEC now does, and if the B1G teams have the same number of them, as does the SEC with it's three perma-rivals per team. 

TBH, I don't know and don't care enough to look it up.  I don't think it is that many though (except for the Western teams who have each other = 3) because with 18 teams and 3 perma-rivals and 9 games that works out to:

• 17 potential opponents
• 3 each year
• 14 rotational
• 9 games-3 permanent rivals =6 to schedule

You aren't playing those other 14 teams very often.  

If you have two permanent rivals as @847badgerfan stated that Wisconsin does then you get:

• 17 potential opponents
• Iowa and Minnesota each year
• 7 games left to schedule against 15 potential opponents so you almost play all of them every four years, you should only be missing one.