Going to go all BobC on BobC with a long(ish) post full of as many questions as answers.
I think part of the problem often is defining your search terms. As a buyer when questing for an item, if I use very specific search terms, then what are the odds that the seller will actually know what they have, and will use the right terms when they list the item?
On the other hand, if I cast a very wide net, then I end up getting emails every second of the day.
A couple of examples of this phenomenon come to mind. You will recall a little while back we had a bit of a kerfuffle over an auction being outed. Which one, you may ask? There was a Babe Ruth item, where the seller didn't know what they had - they just listed it as a Babe Ruth baseball card.
Here is the thread:
https://www.net54baseball.com/showth...e+ruth+auction
Or you can also think of the seller who listed 4 Topps Dice Game cards on eBay for $4.99, not knowing what he had, and so not referring to them as Dice Game cards.
Here is the thread:
https://www.net54baseball.com/showth...ight=dice+game
The point being that saved eBay searches only really function well when the seller actually knows what they have, and correctly lists it. Barring that, your quest for a particular rare item requires that you wade through a tremendous mountain of eBay listings to find that needle in the haystack.
The other element that comes into play is that sometimes the one thing you really want is buried in a larger lot. Someone might just list "Big bag of old baseball cards", with a few pictures. And the one piece you've been questing to find for the last 20 years is buried in there. If you're lucky, they include some pictures, which might help you to find it, but only if you're willing to spend the time looking at a lot of listings and staring at a lot of pictures.
In terms of searches across auction sites, the closest you might get is some sort of a google search that pings you when new web pages come online that include your defined terms. It's been a while since I last attempted it, but if you're looking for something really specific, it seems like this might work for auction sites.
Here's a webpage that describes how to do it:
https://support.google.com/websearch.../4815696?hl=en
Might not be perfect, but it might be the best we're going to get until someone a lot more tech savvy comes along and creates a tool to search across different auction sites.