I'm not sure if you are having a "new" problem, or this involves a car that's been sitting.
In my '69 I had similar problems, but my car had been sitting for 15 years.
I removed the sheet metal shifter cover and drizzled as much kerosene down into the shift linkage as I could while "working" the shifter gently back and forth. This took a fair amount of time, but it kept getting better and better. I was worried that it was a bent shift fork, but I figured I'd have to take the trans out anyway if that was true.
By the way, I tried to remove my shift lever by removing the ball ring and three retaining bolts (it's supposed to be "easy" to remove and looks just like the design of my Sprite which I've had out dozens of times). Anyway, I was never able to actually remove the shift lever (it was somehow "stuck" I guess). But the combo of gently "working" it and the kerosene got things to work fine. I'm sure a lot of the kerosene made it's way into the trans so I changed the trans oil when this was done.
G'luck.