There were two versions on the 9 speed RD made, with slightly different actuation ratios. The early model would probably match your 8 speed, but the newer model requires less cable pull and would probably over-travel a bit.
I can only encourage you to move on to a newer drivetrain, since 8 speed was replaced by 9 speed, 15 years ago. 9 speed was replaced by 10 speed, 12 years ago.