I think we would need to see the item number, to read the ad to see if if was actually being passed off as a logitech mouse or if it was advertised as unbranded but compatible with logitec or whatever.
Some ads on ebay can be very deceptive to new buyers. I have to say those ads are usually from Chinese sellers though, who might use a brand name in the title but when you see the item specifics, it becomes clear that it is unbranded.
You say you initiated the refund process but I hope you didn't do so on the claim it was fake, because unless you can prove it, you may lose. Better to open with not as described or faulty. Too late now.
See how you go, anyway. Not all sellers ask for the item to be returned. If they do, be aware they need to pay return postage, not you. Insist on it. If they won't, let ebay know within your claim.
Tempting as it may be to you to cut the cord, I would advise against it because I presume you never opened a claim against the item on the basis of any damage, so the seller would be able to say that it was not received in the same condition it was sent.
Your main priority is to get a refund. You can leave feedback, be very careful how you word it or the seller may have it removed. After that, let other buyers look after themselves, just concentrate on getting your refund.
