There is no eBay provided way to do what you want.
There is probably a way to do it using user scripting (A GreaseMonkey Script that requires the GreaseMonkey addon in Firefox, or TamperMonkey addon in Chrome). A very simplistic approach would be to flag (a checkmark or make it partly transparent) or hide completely any search results already viewed based on sniffing the fact that the link shows as visited in the browser history, but that has a lot of problems. A better approach would be for the script to flag/dim/hide search results when user clicks a script added checkbox to the result, and then undo the flag/hide/dim when user unchecks the checkbox. That would require script to maintain an external blacklist, and managing what is hidden and what is not would get messy.
No idea if anyone has done this already (doubt it), but as I said, it would require use of FireFox or Chrome, installation of user script addon, and then installation of the hypothetical script. IE, Safari, Edge browsers are out of luck.
https://userscripts-mirror.org/ (mirror of old, no longer up userscripts.org) or
https://greasyfork.org/enI usually do my crude filtering by observing whether or not the listing link in search shows as visited (turns purple). I use a Firefox addon called LinkVisitor that allows you to mark links as visited or unvisited in the browser history using the keyboard. I also use a GreaseMonkey script I wrote called SellerSnubber to blacklist sellers by username (mostly if they are flooding a search or category with lots of items I have no interest in). Not as elegant as the functionality you are asking for, but suffices for my needs.
It would probably be a bit more trivial to do some cosmetic things (add some text, a graphic, bolding) to search results to make it more obvious they were looked at based on if the link was visited using just CSS, but, that requires either using Stylish addon in Firefox or Chrome (or inserting the code into a Firefox usercontent.css textfile). IE Safari, and Edge out of luck again.