Problem getting to big ring with XTR M960 Shift Lever
Finally found the right combination of Google foo to find what I was looking for.  This Youtube video breaks it down that old grease in the shifter is keeping the teeth from catching.

By spraying WD-40 into the housing via the inner cable hole.  Let it soak a bit, and work it in via shifting up and down.  It may take a few minutes, as mine took 5-10 minutes and a couple of treatments but finally it started getting the big ring click.

After the WD-40 is dry, then lube the inside of the shifter with a regular lube to keep it operating well.