Use less oil on the chain. A tiny drop on each roller is all you need. Then you’ll never need to clean it. Honest.
You can put the $12 toward a new chain, and here I’m not even asking you to accept shorter chain life from not cleaning it: it’s not going to be dirty, right? If it’s dry, I oil it. If it isn’t, I don’t.

In the old sailing Royal Navy, ship captains would grouse that the King’s tight-fisted Admiralty purchasing agents would “waste a ship to save a ha’penny-worth of tar.” Fair enough, for ships. But if ships were cheap and built to wear out (like chains) and tar overpriced and expensive (like Park fluid), the calculation would be reversed.

I don’t have any cleaning solvents on the bench anymore. I can’t remember when I last cleaned a chain. Yes if I rub my fingers on it they’ll come away black, but so what? It doesn’t look dirty, and only Freds touch their chains. Elbow grease and rags of various descriptions, including shoe laces, are all I need for cleaning other bits. Small screwdrivers are handy to remove “dental plaque”, that dry-paste mixture of oil and steel dust that builds up on parts adjacent to where the chain runs. You want to scrape this stiff off intact into dry hard little piles where you can sweep it up. Where it is it isn’t doing any harm. If you liquify it with solvent it goes everywhere into the moving parts where you can’t get it out and makes everything filthy.