Was the refund done through a case the buyer opened? Proof of postage means nothing in those cases, it's tracking which shows delivery which will close that case in your favour.
It doesn't matter what the buyer informs you of the tracking they received, telling you there are 2 is not correct.
Was this a Royal Mail delivery, you could have checked the tracking on their Track & Trace online and that's the one which matters.
End of the day if you had tracking to show delivery and entered it into the case , you would not have had to refund.
If you now have found that tracking has shown delivery contact eBay Customer Services see that they say.
This is the easiest and quickest way to contact eBay Customer Services, for a Call Back option.
https://www.ebay.co.uk/help/eua?id=5275&mkevt=1&mkpid
Lines open 8 a.m. - 10 p.m. on weekdays
9 a.m. - 6 p.m. on weekends.
Automated agents will be available on chat outside of the above hours.
I do recommend contacting CS very first thing in the morning, when the lines first open, as there's more chance of Dublin answering.
@hayley_knapp1