I have no experience with your particular model, but do have considerable transmission experience, and can say (for near certainty) this is not a "split the tractor" problem. It is (almost) for sure a shifter - linkage problem. Typically the shifter reaches the 'neutral gate' before the forks actually fully disengage the 'active' gear (this instance 3rd gear). There is a safety feature in the transmission that prevents more than one gear (at a time) being selected, so why the shifter "thinks" the transmission is in neutral, it is in fact still in 3rd.
It can be caused by wear, or linkage coming loose, or something jamming the linkage.
It was not clear (to me) if (1) you cannot get the "shift stick" to move to neutral, or (2) it does move into neutral, but the transmission remains in 3rd.
If (1), probably something is jamming the shifter or linkage. This could well be something inside the transmission cover plate, and be a bit complicated to explain, and to perform for the first time.
If (2), probably something is worn / bent / or needs adjusting.
If you can still move the "shift stick" (into the neutral gate), try "re-engaging" 3rd gear with the stick, then straight from 3rd, through neutral, and into 4th.
If that works, something is very likely worn (or loose). If caused by wear, you can teach yourself to "work around" the wear; - pull (push) the shift stick well into the neutral gate BEFORE pushing it sideways to go into the next gear (1st or 2nd, in this instance)
Good Luck! please keep us posted on what you find.