phoenix
Never touch anything precious with stone cleaner, these are often acid based. I would not even use a scrubbing brush. Just try a soft cloth and mild detergent. Granite itself is very tough but any inscriptions could suffer.
Many such ornamental materials that are described as "granites" are generally other "igneous rocks" as in much of the stuff sold for kitchen work surfaces. This group of rock types contain a range of different minerals in different proportions. Some of these have a lot of calcium based minerals which could be damaged. Don't bring stone cleaner anywhere near any limestone or marble. Even Sandstones can contain a lot of shell debris. These carbonate materials are easily damaged by any stone cleaner.
I would not touch any gold inscriptions with a tooth brush, just lightly brush dust off with a soft paint brush. It is probably fairly thin pressed on gold leaf.
Many old head stones seem to be made of very poor stone which peel away in layers and cleaning of old stone in likely to leave damage. I think lichens eventually damage stone monuments as they get nutrients out of the stones themselves but that takes a very long time and maybe a natural process that should not be prevented.
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Have any of you got all electric cars? Pros and cons please.