I ordered this around 4 months ago, but it just arrived yesterday. It's called a "Blinking Light Win", and it replaces the snap-down 72 pin connection in an original NES.

It's basically a top-loader connection inside an original NES. The original 72 pin connector and cartridge tray have been removed and replaced with a solid connector (that's always connected), as well as a new cartridge tray. The game slides in, snaps into the new connector, and that's it - no more pressing down to make a connection. The new parts are the same size as the old ones, so everything fits back just like it was before. It took me less than 10 minutes to hook up. I believe it also disables the region protection, but I don't have any non-U.S. games to check.
(I should have taken some photos as I was installing it, but a quick google search will show pictures and videos of this product)
So far, it's worked for every game I've tried, even some that I could not make work before. Since there's no more connection that has to be made, there will never be another blinking light error. The connection is a little tighter than an original 72 pin, but not nearly as tight as an official Nintendo top loader or the death grip of some clone systems. Now I get the beautiful picture of an A/V connection with the reliability of a top loader.
This was a campaign on Kickstarter, and the company that makes it is called Arcade Works. I didn't get in on the Kickstarter campaign, but I was able to order one from the Arcade Works website for $20 + $5 shipping.