Instead of a separate program, many Eaglercraft players use custom clients that have auto-clickers built into the game's GUI. Popular options tested for performance and fairness include: Resent Client Shadow Client Astra Client
5–10 CPS is more than enough for casual play. auto clicker for eaglercraft
When in doubt, read the server’s rules. Most Eaglercraft server Discords have a #rules channel explicitly banning "automation tools" or "macro software." Instead of a separate program, many Eaglercraft players