No, you'll only need to drop the transmission pan.
If you haven't done a fluid/filter change recently, now would be a good time.
The governor is located in the pan, under a four-bolt aluminum cover towards the rear of the transmission. Remove the four bolts and lower the cover down. The governor will come out with it.
The proper setup has a single spring between the governor shaft and the lighter of the two weights. If your spring is not there, that is your shifting problem.
Donald Wang in CA has governor springs made up, I believe, if you need a replacement.
