If it goes past the 4 (I thinik it is) days you are given to solve the case, it is then open for the buyer to escalate.

Regardless of what has happened in the case to that point if you have no tracking then ebay will surely find in favour of the buyer and will simply refund. If they do this you will certainly be given an unresolved case defect. The worst and most damaging kind.

You could just wait if the buyer is being unresponsive. It's possible they have since received it and have simply not bothered to do any more about the case. If you wait and they never do anything then 30-business days after the last correspondence from them the case should automatically close in your favour. But by waiting you run the risk that the buyer could escalate at any time.

We had a similar one recently and just refunded after the four days as it was only $8. But our buyer responded saying she would prefer a replacement be sent out. But as we use untracked large letter this was not an option with the case still open as she could still escalate and get a refund as well. We asked her to close the case before we would send the replacement, but there was no more heard back. After we refunded she left us NEUTRAL FB saying item never arrived but she received a refund. So we blocked her across ALL our IDs. If she wants that exact item (handmade and unique to us) she will not get it now.

Never escalate the case yourself as this will definitley cause you grief. They will close it in the buyer's favour immediately.