On my new coach, where the ac was not properly tightened I had some yellowish stains. I got rid of them with my bissel carpet cleaner upholstery tool using the citrus machine shampoo from walmart.
Sponges and a one of the spray carpet cleaners should do the same. I don't think I would use a stiff brush on the ceiling covering.
I only use the upholstery tool now with that machine as it ruined my hardwood floors. The water from the unit got into the foam layer under the carpet and stained the wood deep enough to warrant replacement as they spots are too deep for sanding.
2011 Allegro 32CA \ 2013 CRV toad
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99' Winnebago Adventurer /Towables