Usually you push the shifter and it springs back with no gear shifting. You tend to find this more in cold weather or not having been used for a period of time.
I would say this is your problem but you say it doesn’t snap back.
Does it feel like the spring has gone and the lever is floppy or is there resistance there that stopping it snapping back?
It’s probably the grease gumming up the pawls.
They tend to do this at 20+ years.
Usually you push the shifter and it springs back with no gear shifting. You tend to find this more in cold weather or not having been used for a period of time.
I would say this is your problem but you say it doesn’t snap back.
Does it feel like the spring has gone and the lever is floppy or is there resistance there that stopping it snapping back?