If your customer has opened an Item Not Received case against you then unless you can supply eBay with solid proof that the item has been delivered to the address that the buyer supplied at eBay Checkout then first of all try contacting your customer via the case to see whether he or she would be willing to accept a replacement item. If, however, the buyer is unwilling to accept this option and replies with something along the lines of "I just want a refund of the money that I paid for the item that I never received" then you should refund the buyer in full within three working days from the date that the case was opened on. If you leave it longer than this and fail to refund the buyer's money then if he or she escalates the matter to eBay in order to get them to step in and resolve the matter then eBay will just force a total refund of the money that the buyer paid for the item and your account will be hit with a selling defect, which is something that you should be looking to avoid being slapped on your account if you wish to continue selling on eBay in the long term.
With regards to the point @moldosgifts raised earlier in that you are a businesss trading on a private account you need to either upgrade your existing private account to a business account, or alternatively open a second eBay account and keep the first one as a private account and set the second one up as a business account, or vice versa. That way you can keep your eBay private buying account activities completely separate from your eBay business account activities; however, you will need a separate e-mail address to link up to the second eBay account. If you fail to do so and continue to trade as a business seller on a private account then you will eventually come unstuck, especially if you go above the annual limit that you can earn before having to declare your earnings to HMRC.
