i prefer turning pilot off when not needed for a couple days. waste of gas.
corrosion i could never buy into that. granted i would imagine some areas of the US and world in general, some metals in some locations may be more prone to rusting vs others. but it would still be a hard sell to me. on other hand "dirty air" of fresh air being drawn in to keep pilot light going, and mucking things up i can believe. a couple vent-less heaters for 15 plus years, between summer/winter usage i can see the difference between turning off in spring and cleaning, and then come fall and cleaning before start up, there is a difference.
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as far as how much fuel a pilot light uses "depends"
a full tank of 20lb cylinder = a higher PSI being pushed to the pilot as a result more fuel is used to keep pilot on.
a tank that is about empty = less PSI being pushed to the pilot as a result less fuel is used to keep pilot on.
granted a regulator between tank and pilot light, keeps more of a steady pressure going to a pilot light when tank is full vs nearly empty. there is still a difference, regulators are not "perfect devices"
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this last cleaning on ventless heaters, used "kaboom" purple spray can, for cleaning kitchens / bathrooms. sprays a blue foam on, and within a few seconds turns white. only thing i have found to actually clean all the nook and crannies so much better. first time seeing nearly perfect flame "pilot and burners" as if they were new, vs being 15 plus years old.