Old gas leaves gook commonly referred to as gum and/or varnish. Not sure about "wax" but whatever.
I've just been dealing with that exact issue. I'm resurrecting a freekin' Gold Wing which has been sitting for many, many years (10?) but not pickled for storage.
#4 carb needle was stuck open, dumping much raw fuel into intake and some made it to crankcase too I'm sure. Yeah, motorcycle carbs... I only wanted to drop the float bowls and examine floats and needles BUT NO, the manual says disassemble the entire motorcycle to get those bowls off cuz the carbs are all siamesed together!
To **** with that, with the ingenuity of MacGyver and the skill of a surgeon, I removed the worst offender's bowl, swiped a mirror off the x-girlfriend's makeup compact, and got er done with no other disassembly. Oh... right... the point of the post. Lots of gum and varnish kept the needle from moving up and down in the seat. Had to physically scrape it off (knife, scotchpad) and chemically clean the rest of the residue with carb cleaner. Sparkplugs told me the right bank was OK, so that left #2 as "doubtful". Got some gas additive "carb cleaner" and let her have a super concentrated shot of it.
3rd day now and it's running fine!