OK, I'll let the Internet in on a little secret. Do yourself a huge favor and grab the Universal Cleaning Kit by Performance.
https://www.ebay.com/sch/i.html?_from=R ... itleDesc=0You have to go used or NOS because these things haven't been made since the 90's. But they are simply the BEST way to clean cart slots. FWIW, you can easily replicate this same method at home, but it's a lot easier to just buy something. Whether you buy new or used, the cleaning solution will probably long since evaporated. No bother, just use isopropyl alcohol (as close to 100% as you can).
If you look at the picture on the front of the box, the bottom-right corner are the cart slot cleaning tools. Nintendo carts have a different PCB thickness than Genesis, so important to use the right one on the right console. Anyway, the ends of them have this sort of vinyl material on the ends of them. You wet it with some alcohol, then insert it into the cart slot. Pull it out half way, then push it back in. Repeat this motion a number of time. When you pull it out, you should see some gunk on the end. If it's still wet with alcohol, you can easily wipe it off with a rag. Repeat this until you can pull it out and no more gunk appears (that's at least a good visual that the slot is relatively clean).
Again, look at the picture on the front of the box. The bottom-middle, those are this nifty cleaning wands for carts. It makes cleaning cart pins very easy without having to open the shell. Only use these if the pins are dirty to a minor degree. If they need some serious scrubbing, you're better off opening the cart and putting in the elbow grease. These little pads in the Performance kit will wear out fast if you try and use them on heavily corroded pins.
Again, look at the picture. The almost dead center is a white bottle. This is the "cleaning solution." Just to the left of that is another cleaning wand. This one is specially for the "Super FX pins" on a SNES (those extra pins on each side of the cart slot). To the left of that is some wacky thing that I've never used. Is it for cleaning CD lens? That's more easily done with some alcohol and a Q-Tip.
FWIW, the cleaning wands for the carts slots that are in this kit can easily be replicated at home. Replicating the shape isn't the hard part though. You want the perfect thickness. Too thin, you wont be cleaning the pins very well. Too thick and you can damage the slot. NES and SNES cart PCBs are 1.2mm thick, Genesis PCBs are 1.6mm thick. So you would want something that's pretty much that exact thickness.
Another home method would be cardboard. I remember some people suggesting use cereal boxes and stack layers until you get the desired thickness, then saturate it in alcohol.
But yeah, this kit from Performance has been my go-to kit for cleaning retro games and consoles for decades now. The only pain in the ass is the front loading NES. You can take the shell apart and clean the slot that way. Or just get a NES cleaning kit. But other than that, this kit is perfect. I've considered (perhaps with a Kickstarter) recreating this kit (and even improving on it slightly) to sell.