I am 71 years old so do I check off "not eligible for exclusion for those over age 59 1/2" for my pension from NY?

No - Check the box "none of the above" and make sure the full amount of your NY pension in shown in the New York distribution box.

If you check the "not eligible for exclusion for those over 591/2, then your NY pension would not be eligible for the NY retirement exclusion on your NY State income tax return (and you don't want that).