The knob is a potentiometer and the circuit reads the resistance value to determine which model to select.

In the old Variax 500/700 there was a knob calibration procedure, but that was taken out of the 300s and 600s.  I don't know of a knob calibration procedure for the JTV.

Here's a couple of things you can try. 

First, rotate the selector knob it's full range of movement about a dozen times.  What this does is it will clean away any muck (usually caused by condensation and dust) out of the pot that might be giving an incorect resistance value.  Give that a go first because this is a simple solution that often works.

Second is a tip that came from 1oldguitarman and it involves making sure the middle position of the pot corresponds with the middle position on the selector knob.  Personally, I don't think this will help you because if this is the problem you'd be more likely to have an incorrect reading on Custom 1 and Model T as well as Spank, but if the above doesn't help and you're technically minded, this might help you.  The instructions relate to the original Variax and I have no idea how the knob is seated on the pot in the JTV, so while the aim of the procedure is sound, the actual procedure may be quite different on the JTV.  Anyway, here's how to "Split the Difference" on the selector pot.

PLEASE NOTE:  The following procedure will only work if the selector knob has be calibrated around the centre position of the pot, if it hasn't then the following procedure will make the problem worse.  This procedure was designed to improve the calibration process and assumes that you can actually calibrate the knob after completing the procedure.

"SPLIT THE DIFFERENCE":  the model select potentiometer has more travel than the physical detent knob allows.  You can observe this by turning the selector to CUSTOM 1 (fully  counter-clockwise), then very carefully removing the knob entirely from  the stem of the pot while not allowing any pot rotation.  The pot can probably turn further CCW.  If not, place the Model Select back onto the stem, turn fully CW to CUSTOM 2 and pull the knob off.  You'll observe extra travel.  UNTIL I ROUGHLY SPLIT THE "EXTRA" ROTATION DISTANCE BETWEEN CUSTOM 1 (fully counterclockwise) AND CUSTOM 2 (fully clockwise), the calibration procedure failed repeatedly for both of my VAXes.  The procedure resulted, sometimes, in different model selections being missed, but always a model selection would be ignored/missed.

To SPLIT THE DIFFERENCE:

1. Turn Model Select to CUSTOM 1
2. Carefully pull (remove) the knob from of the stem of the potentiometer
3. Turn the pot fully CCW
4. Place the Model Select knob back onto the stem, making sure it's indicating CUSTOM 1
5. Turn the knob fully CW to CUSTOM 2
6. Again, carefully remove the knob from the stem, causing no stem rotation
7. Note how much extra travel the stem can turn to fully CW (you can place a post-it note or piece of tape at the base of the pot and mark the 2 positions, but I simply eye-balled it and got good results)
8. Now, turn the pot CCW, HALFWAY back to its original spot (where it was when you removed the knob at CUSTOM 2 in Step 6)
9. Carefully place the Model Select knob back onto the stem, making sure you don't rotate the stem any and it shows CUSTOM 2

Let us know how it goes for you.

Cheers,

Crusty