The AU Hoovers, Simpson and Westinghouse should not index, they have a solenoid operated brake which holds the tub steady during agitation. The brake on these machines has some slack in it, allowing the tub to rock side to side a bit during agitation, but that is not the same as indexing, where there is a mechanism that allows the tub to turn one way during agitation. If a Hoover or, more likely, a Simpson/Westinghouse is indexing, it indicates wear in the brake band as a badly worn brake is only effective in one direction.
Fisher and Paykel machines, both current models and the older Gentle Annie series, have a completely free tub during wash - there is no brake and the tub can move freely either way. On the Gentle Annie it can only move so far before the agitator drive block contacts the spin drive block, then they drive together for a bit. So on a Gentle Annie during wash the tub rocks back and forth a little and occasionally you hear a slight knock and the tub moves firmly a small amount. This is an accident of the drive mechanism design, not a deliberate action.
Chris