One thing they may not have told you.
When you push/pull that handle... Be in NEUTRAL, move to park after it has disconnected
If it's not sliding, even in neutral, the problem is corrosion on the slide or the "clutch". lubrication (And perhaps cleaning) is the answer.
The cable can corrode, or the hardware on the drive shaft. PB-Blaster or Cyclo Break-Away may free it up, but these are not lubricants (They are penetrates, same as WD-40) Once they work.. Lube as per REMCO suggestions.
Home is where I park it!