L8's have that issue often, just due to the design of the shifter. The later 5000 series improved on it to (almost) eliminate the problem.
Here's my usual plan of battle:
1. Disconnect linkage behind the right tire. Should be two lock nuts(one on a stud and one on a bolt through the shift pin) and the angle pivot will come off. Jack up the tractor so both tires are off the ground.
2. Pull the bolt running through the shifting pin so the pin can rotate free-er. Get more of that penetrating oil and soak the whole thing, especially where the pin works through the axle housing. Work the pin in and out and back and forth and around. These things get gunked up and frozen in place too easily. Keep it oiled and shiny, and you won't have trouble.
3. The shifting linkage can be adjusted at the gas tank. Something I always try is to pull off the nut closest to you operating the tractor on the same eye bolt as the over center spring. That helps guarantee freedom of action.
4. As you tighten things back up, make sure the pivot behind the tire that actually pulls the pin in and out doesn't bind. You have two locknuts holding it; don't tighten beyond holding it from wiggling sideways. It will not come lose.
5. You also have the spring there behind the tire to adjust if you need it. I can't remember without seeing one which side of the shaft does which range. I think the spring closest to the operator dampens high?? The springs "balance" the pivot, so be careful not to adjust yourself out of a high range.
All of these things are "non invasive" attempts. If these don't do the job, there's a high probability of internal damage. 90% are out of adjustment.
I'll be curious to know what works for you!
Ben W. in VA