The BCA no longer controls the Hall of Fame process and BCA members in general do not have a vote. The actual requirements are the responsibility of the USBMA which has a website at:
https://www.usbma.com/index.html
Here are all the requirements for the "Greatest Player" category from what I believe to be the current requirements document:
A) Greatest Player
• Candidates must be at least 40 years old by Jan. 1 of the year of their induction.
• Candidates must have professional playing careers of at least 10 years. A “professional playing career” will have started with the player’s first entry in a professional tournament affiliated with a credible billiard association or promoter.
• Candidates must have recorded significant achievements in U.S.-based events.
The specific requirements are fairly light so the process depends on the judgement of the USBMA HOF Board. "Significant achievements" is the key.