You can replace the alternator as a "maybe", but if it were me I would first check the output from "terminal P" and see what you get. Most electronic tachs on other New Holland tractors operate from AC voltage from the alternator. Very low voltage at that, like 8 or 9 volts. 5 volts is not enough. I know that from experience. This is on other models, not TC series tractors.
I would try to catch it when the tach works and see what the voltage reads. Then again when it's not working and see if there's much difference. The DC portion of the alternator can be working, keeping the battery up, charging at the proper rate and all that. In most cases repair shops only test that portion, and rarely look at the AC tap, so having it tested usually won't catch the problem.