Could be your shifter is installed/assembled incorrectly. Is it an aftermarket short shifter?
There's a video of some guys replacing an S13 shifter that shows some decent views of the components. You don't necessarily have to remove the entire plate if you have snap ring pliers you just need to remove the shifter itself to check if it's aligned correctly (for the OEM shifter). If it's an aftermarket shifter you don't even need snap ring pliers, just an allen wrench to remove the 4 bolts.
>BE VERY CAREFUL NOT TO DROP ANYTHING IN THE HOLE WHEN YOU REMOVE THE SHIFTER. ALSO IF IT'S A SHORT SHIFTER BE VERY CAREFUL NOT TO DROP THE SPRINGS ON EITHER SIDE OF THE SHIFTER AND REINSTALL IN THE CORRECT SEQUENCE.<
I can't stress that enough. It's super easy to drop stuff down there or lose the springs and put it back together wrong.
I'm guessing that's your issue but, in any case, it's the easiest thing to start with because more invasive checking is going to require you to pull the transmission again.
better view of removing the OEM shifter