If warranty and proof of purchase were important factors, why only ask now, and why even bother looking at ebay in the first place?
As mentioned above, unlikely that the warranty would be good for the second owner, but check anyway. It’s worth mentioning, in relation to warranties, that the good companies will often honour warranties even when they don’t strictly have to, and others will try pretty much anything to avoid helping you even when you have a clear warranty issue and bullet proof paper trail.
I’d be happier buying an open box product off ebay from a manufacturer with a good customer service rep (like Garmin), than a brand new product from a proper retailer if the manufacturer is a PITA to deal with.