Why won't my tractor stay in Neutral when put there? Why do I periodically lose reverse? Why does it go forward while in reverse?
You could post up the full technical model number from under the seat, that number might actually permit one of us to view the parts for your specific DYT4000.
What you have posted so far is like describing an automobile as a Chevrolet Impala, without including the other numbers (year model and V.I.N.).
The full technical model number will provide what is needed to look at your parts.
917.273640......guess i could have included this
There are a few possibilities, all having to do with excessive wear or loose fit in the directional control linkage.
My first suspect would be the control arm on the transaxle case where the directional control linkage ends at the transaxle.
The control arm attaches to the directional control shaft (aka swash plate shaft) with a bolt.
The control arm has a square shaped hole and the control shaft has a square shaped profile where the two fit together.
It is possible that the bolt holding the control arm to the control shaft has been loose and worn away the profile of the two mating parts to the point that the control arm and the control shaft are no longer locked together, but instead are now able to allow the control arm to move (when you move the directional control lever on fender) without affecting the same movement to the control shaft.
This is going to require a close up visual inspection of the control arm where it attaches to the control shaft while some body operates the forward/reverse lever to determine if there is a lot of slop between the two components. Normally, there should be no lost motion between the two parts.
You may have to remove the bolt that holds the control arm to the control shaft to see if the square hole and shoulder are no longer "square" because of wear.