I sould suspect a universal joint or CV joint problem first. You may even want to roll down all the windows and list for the squeak when accelerating and braking and the transmission is not shifting. A good way to test this is to drive down a narrow street or alley where there are buildings on both sides. The noise becomes very obvious as it echos off the buildings.
It can also just be an engine or transmission mount causing the squeak. It only does it on shifts because thats when the tension on the mounts changes. Shifts into 5th gear or O/D are not even perceptable and not enough flexing occurs to cause the squeak.
It could even be a body, chassis/suspension that is generating the squeak when the transmission shifts for the same reason an enigne or transmission mount.
The rubber may have deteriorated, or the component is a little loose. I seriously doubt that the squeak is actually comming from inside the transmission, or that you would even be able to hear it if it was.
...Rich