Been there. Only thing that works is heat. Use a plumbers propane torch and heat the area (carb out and drained of fuel). Careful not too hot though. If you start seeing sparks it is beginning to melt. Get the area good and hot and pull on the cable. Should come out. Some welding gloves will be helpful. Chem dip the carb for a few days while waiting for a new brass plunger and seal kit. Use a small barrel brush to clean the hole when it comes out of the dip. Will be ready for another 30 years.
Trikes: All Honda: 84 250r, 85 86 and 87 250sx, 84 and 85 125m, 79 82 84 and 85 110's, 73 us 90 and 77 atc90, 75 atc70
Cycles: Honda: 71 cb100, 78 cb750 coming soon cb750 trike. Yamaha: 67 yds 3 (250cc, 2cyl, 2 stroke), 82 750 SECA
Other toys: Chenoweth VW sandrail dune buggy, old race go kart, racing mower, 76 Arctic Cat Pantera 440 snowmobile
KEEP IT ON ALL 3 OR AT LEAST 2 AT A TIME