You may want to first, check the signal on the yellow/green wire from the ICM; you need some way to measure the peak voltage of the signal while the engine is running, which should be greater than 10.5V, relative to the green (ground) wire. You may also want to verify the +V is steady on the black/brown wire.
Thanks for the tip. I loosened and then tightened the connections inside the tach, reassembled, and now the tach does go beyond 3k. Go figure. Gonna keep an eye on it for now.