I don't see why it's impossible to come up with a decent set of rules for behaviour that aren't dozens of pages long. Of course, I've never tried so what do I know?
Happy to offer opinions on any attempt to do so, however!
The good thing about zombies are that they are mindless so AI isn't really necessary. Just set them loose and the go for the closest without any concern for themselves.
That's still 'AI' though - just because it's not complex it doesn't mean there isn't a 'program'. For a zombie it's something like:
1 - determine nearest target;
2 - attack;
3 - ignore wounds/morale tests;
4 - until target or zombie is dead;
5 - got to 1 if zombie is still functioning.