Our tried and true method is to remove the covers, saturate the mechanisms with PB Blaster, working the shifter and pawls for a few minutes. Finally follow up with a squirt or two of the 3-IN-One lightweight penetrating oil. Work the shifter again and magic. This stuff is gold for these shifters.
Available at Home Depot
https://www.homedepot.com/p/3-IN-ONE...0015/300719551