I'm going to try & write this as simply as possible as earthdog has already said we have confused him. Hopefully this will summarise the techy advice above in followable steps.
The guys are saying your cable connectors look like the box is in "full throttle forward", even though the lever is in the neutral position.
So, follow this step by step:
With the control box "as is", disconnect the cables at one end. (this will take the engine out the equation, doesn't matter which end you disconnect)
1) With the lever in Neutral position, can you engage F & R without lifting the red catch?
If Yes, when you moved the lever across from the other side, there is a white plastic "half moon" with a notch that lives under the lever, held in by 2 coutersunk screws. That should have gone too - move it now!
If no, you know Neutral position on the box is allegedly where it should be.
2) With the lever in neutral position , can you lift the fast idle lever and (pull the deadman before you try this one) - will the engine starter turn on the key with the shift lever in neutral?
If yes to both, then there is something likely wrongly assembled inside the box. Post back as that will take a bit of explaining. (but as you presumbaly haven't taken the innards apart I doublt this will be a "yes")
If no to either (more likely both), then unscrew the lever, move it 90 degrees (to WOT F or R, my money is on F), screw it on & pull it back to neutral. (If it doesn't go back to neutral, put it on the other way).
Try test 2 again. Once you get the fast idle lever working & starter turning with the lever in neutral position, re- connect the cables & if it all seems to work properly-ish, fine tune the cables as you have been.
It's the thing with those boxes that the lever can be mounted at 90 degree incrememnts relative to the gubbins inside the box. I have an old 1960s Teleflex control that you could put the lever on upside down if you wanted! Idea being you could mount it with the cables coming out vertically & still have a "conventional " lever position.