NCL is National Chemical Lab and they are located in Philadelphia. Here is a link:
Their ceramic polish is used much like 5x but for ceramic. It is a cream. It helps to have some weight. I will say that it has done a great job for me on some pretty beat up and dirty tiles. The question is whether you can exert enough pressure on a wall tile with an angle grinder to really get it to work. But it is inexpensive and worth a try. The downside is that it is hard to get the stuff out of grout, but if after cleaning the grout there is residual, you can use an efflourescence remover or color enhancer to bring back the natural color.
Their products are fairly easy to get around here in their home town but I've heard that it is harder in other places.
I think the floor tiles in the picture I sent you are about 4" or so. In the days before acrylic enhancers etc, they would treat the floor constantly with Boiled Linseed oil to bring up shine and reduce effliurescence. Not so much for cleaning except that rubbing tiles constantly with that stuff I'm sure cleaned the tiles. Of course, Boiled Linseed Oil is highly combustible. You can mix it in various ratios with mineral spirits.
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