have still to vs still have to

It's not "still have to" because, in this case, the placement of still is optional; it can go before or after the verb.

My guess the rule is it goes before the verb, but still makes sense when used after. It's like six of one and half a dozen of another.

The meaning is slightly different.

The "have still to" form means that the action is required and as yet not performed.

The "still have to" form means that the requirement for the action is still in force. It does not say whether the action has been performed in the current instance.

Example: You cannot go to your party yet. You have still to clean your room.

Your room must be cleaned before you go to the party. You have not yet done so.

Example: Now that you have reached the age of 16, you have some additional privileges. But you still have to clean your room before you go to any party.

The requirement to clean your room has not been removed. There may or may not be a particular party being discussed at this time.

Current best answer appears to be by user339660 almost a year ago in comments. So moved to the answer below:

Still can go in either position but still have to is much more common.

Have still to can sound quite stiff and old-fashioned but it is still used.

There is a slight nuance in that:

They still have to X

Means they have to X and they haven't yet, whereas:

They have still to X

Can just mean they haven't yet X (like they have yet to X, which doesn't imply any obligation at all).

In this context there isn't really any difference between those meanings and I would say it's just a question of style.