Well it looks like it's the transmission. I disconnected the cable from the transmission and it moved freely when I pushed/pulled on it. Unless someone has other ideas it looks like my local transmission shop will have to take a look.

 

The next step is to disconnect both cables at the transmission and shift the transmission. The transmission will be difficult to shift by hand. The neutral gate will be easier than the 1/2, 3/4 & 5/r. Since your problem is the neutral gate I would start there. The transmission itself may or may not have a spring centered neutral gate. I have never worked on an S series manual transmission. However I would study the linkage see what you have before taking the car to the transmission shop. It still might be a cable stretching. The cables do not appear to be adjustable in the pictures I have looked at.
An easier test might be to connect the cable at the transmission and pull the cable farther than the shifter can pull it inside the car and see if you can get to the 5/r slot in the neutral gate.

 

I just looked at my cable shifted F35 transmission that fits an Ion redline. One arm for the 1/2, 3/4 &5/r cable has a big balance weight . The other arm is for the neutral gate. My transmission is spring centered to the 3/4 gate. It moves one way for 1/2 and it moves farther the other way for 5/r. On my L reverse is farther over than 5th so that makes sense. If you select the 1/2 gate and shift the trans into gear it holds the gate until you shift back into neutral the the gate recenters. It works the same on the 5/r side.

 

Well, I reconnected the cable at the transmission and then pushed/pulled the cable (the cable on the near side of pic #1) to no avail. It never moved at the transmission side.

 

I though I replied last night.
Have you disconnected both cables at the transmission end yet? See if the neutral gate lever moves both directions from a spring loaded center position. If so it probably just needs cables.

 

I only removed the cable from the transmission side (the shift tower side was already disconnected) to see if the cable would move freely when pushed/pulled from the shift tower side. It did. I can disconnect the other cable from the transmission but, honestly, I not sure how to shift the transmission manually. I'm really not up to snuff on transmissions. You may have to elaborate on your comment about "See if the neutral gate lever moves both directions from a spring loaded center position". I definitely appreciate you input. I believe that the neutral gate lever is from where I removed the cable which is top lever as I'm looking down from the top.

 

First thing is to make sure the transmission is in neutral.
Let’s start with the lever from the first cable that you disconnected at the transmission. That is the neutral gate lever. There is neutral between 1/2, 3/4 and between 5/r.
The lever is spring centered in the 3/4 part of the neutral gate. When you move that lever you will feel spring resistance in both directions. It will move one way further than the other at least mine does.
When the cable pushes the lever the the transmission neutral gate moves to the 1/2 section. Now if you move the shifter in the car forward the transmission will shift into 1st gear with the other cable. Put the car back in neutral. You will not be able to move the neutral gate lever if the transmission is in any gear.
Now try moving the lever in the other direction. This is the problem area for your car, this is the 5/r part of the neutral gate. If you can move the lever in this direction against the spring have someone pull back on the shifter. This will shift the transmission into reverse. Start the car and see if it is in reverse. Push the shifter into the neutral position. Let me know what you find.

 

Here are two pics I took. Although the first one shows the cable removed from the lever, once the cable was reconnected the lever never really moved much (at all) past where it is in the pic. The second pic shows the lever being pulled as far at it would go to the right to show how much more room the lever could move until it was at full stroke.. Now, when the cable is connected to the neutral lever, the shift tower moved to the full right side and would not move into the left side (1/2 gate) position. In other words, you could move it to the middle (3/4 gate) and far right but not the far left. At this point you'd swear it was in the 5/r gate but putting it in reverse position (far right and down), the car still moved forward. If the cable is disconnected the shift tower has full movement from left to right but it still moved forward when it was in the far right (5/r) gate. I thought that disconnecting the cable and pulling the neutral lever as far as it would go (pic #2) that it would get it into the "actual" 5/r gate but, alas, no. Still moved forward. I have not, to this point in time, disconnected the lower transmission cable during all of this testing.

Top shift cable next to neutral lever

Neutral lever pulled to the far right

 

Is it possible the the lever is supposed to be one more groove out from the transmission? It looks like the arm is against the case in the first picture. Maybe Derf can look at his SC2. I will PM him.

 

This is a picture of what you should have. Notice how this compares with your pictures. Your linkage at the transmission is in the wrong place. Something is worn and slipped out the correct groove. Hopefully it is all external and an easy repair.