There are a wide variety of opinions on changing AT fluid if it's been neglected and in very bad condition. But the fluid would most likely not be causing your shifting lever problem. Sounds more like the mechanical cable is binding. The cable runs from the shifter lever thru the firewall to the neutral safety switch on the transmission. My guess would be either the cable is binding or the switch itself needs to be replaced.

If your HL has a dipstick for the AT, pull it out and wipe it on a clean white cloth and smell it. Color and odor can determine the condition of the existing fluid. Post back your results.

 

If you do ANY change related. Use the Toyota fluid and only Drain and Fill. This is extremely important. It will mix, blend in with the existing. You can do another drain and fill soon after sufficient driving to blend in more clean quality fluid. NOT DRAIN AND FLUSH or 3rd party fluids. Certainly not now as you need to minimize the stress on the system with anything totally different since the fluid is that old.

 

Highly recommended to do what Tripplec just posted. You will notice your transmission shift smoother and faster. If your fluid is not a bright cherry red color, it is long overdue for a change. Just a note regarding checking the fluid level. Always check when the fluid is at or above 80c, engine is running. The transmission can be sensitive to incorrect fluid levels.

 

I would change it few times with OEM WS fluid (drain and fill), better yet, change the transmission filter as well, and clean the magnets in the pan. That's what I did with my 2010. Works well.
I bought AISIN WS transmission fluid from RockAuto.