Long number person --

Unfortunately you formulated the problem incorrectly, to the extent that Sarah cannot arrive at the correct answer. Here is what you had one of the heads saying:

And I should warn you that one of us always tells the truth, and one of us always lies. That’s a rule too. He always lies.

If the head imparting this important information is telling the truth, the scenario can play out substantially as you have set forth.

But what if the head giving this rule is the liar? If so, everything thereafter is indeterminate.

To wit:

If the head is lying about the phrase one of us, then the sentence becomes (when reversed to reverse the lie) Neither of us always tells the truth and neither of us always lies. Or it could be both of us always tell the truth and both of us always lie.

If the head is lying about the second conditional (always) then the true sentence would be One of us sometimes tells the truth and one of us sometimes lies.

If though, the head is lying about the third conditional, the opposite becomes: One of us always lies and one of us always tells the truth.

In previous versions of this puzzle that I've seen, the information about the lying head and the truthing head has been imparted by another party. Only in this way can your contestant always arrive at the correct conclusion.

TEd