Yes, that's what you need to do. You can take the driver board from your tach and install it onto the '89+ tach.
NOTE: The instrument itself may have some variances. My tach now reads low, and if I rev it to an indicated 6,000 RPM, I'll hit the rev limiter, which I believe to be at 7,000 RPM. Therefore I never take my car over an indicated 5,500.
This is with an '89 NA tach with an '87T driver board.
When I installed the '87T tach with the '89NA needle and face, the tach would indicate 8,000 RPM at what SOUNDED LIKE 6,500.
Using a calculator for speed/RPM using the 3.909:1 diff and 225/50R16 tires, and using 4th gear (1:1 gearing) at speed (verified by GPS) indicates that my tach is now reading about 18% low, which is about what I expected, given the evidence. I did not run the same test with the other tach, though I still have it, and may try it again one day.
I surmise that the '87T tach may be balanced for the needle that came with it, and the '89 style needle has a different balance, which may be throwing the instrument off. This does not, however, explain the error with the '89 instrument, unless there's also a change in the driver board. I don't know for sure, but I'll eventually want to replace my tach with an accurate one. In the meantime, mine works, and I can "translate" it to reality fast enough for the only thing that really matters: Redline.