Disassembly.
Chemical (Chem-Dip) and ultrasonic cleaning.
This video shows the tools you need and how to take apart the Keihin butterfly carb as used on 1976-1987 Harleys. Emphasis on Iron Sportsters (1957-1984).
Transcript: https://www.open-sport.org/Repair/Keihin-carb-repair-2/
Help a brother out, some Amazon associate links that pay a percentage of anything you buy during the same browser session.
A rebuild kit with Viton needle:
https://www.amazon.com/exec/obidos/ASIN/B009CA2SEU/cookinexperi-20
Rebuild kit just for accel pump:
https://www.amazon.com/exec/obidos/ASIN/B00HXJAP2O/cookinexperi-20
the Viton O-ring:
https://www.amazon.com/exec/obidos/ASIN//cookinexperi-20
Clamps and O-rings:
https://www.amazon.com/exec/obidos/ASIN/B009BQXBH8/cookinexperi-20