We just use any common septic system safe. often single ply, TP, regardless of brand name. We have tried the RV TPs but have found that they will disintegrate while using it but not necessarily in the black tank
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As far as that shake test - not really a valid test as I don't know of any time while parked at a CG or even driving our nation's crappy highway system that our 5er has shaken that violently so any TP will seldon fall apart easily. A macerator along with a couple flushes ( or outlet end back flushes ) will clean out any building poo pyramid.