Firstly, make sure that you have uploaded the tracking number to eBay (which you should do when marking items as dispatched). If ypu don't know how to do this, see: https://www.ebay.co.uk/help/selling/posting-items/tracking-items-youve-sold?id=4088
Next, ask your buyer to open a case under eBay's money back guarantee, through the resolution centre.
EBay can't and doesn't attempt to investigate deliveries. They will check the tracking number, and provided it confirms delivery to the buyer's address they will find in your favour. You won't be required to refund the buyer; just as important, the buyer will not be allowed to leave you negative feedback (or any left can be removed).
Unfortunately for buyers, there are often problems with deliveries. Anyone can sign for parcels, it doesn't have to be the buyer. Some services don't even require a signature. Parcels may be delivered and signed for at the wrong address, or left in a "safe place, where they may be lost or stolen. Doorstep theft of parcels has soared in recent years.
Obviously, if there's anything you can do to claim compensation for the buyer from Royal Mail or the courier you should do it, but if the parcel has been recorded as signed for they're unlikely to accept responsibility.
