You're right -- there are at least five John Livingstons in Pennsylvania units.

To determine which unit this man joined, you might check for a pension in this man's name, which can be done here. Pension applications may include facts that you listed, plus his residence at the time of application. You listed a street address but not a city, state and date of residence, all of which would be useful.

That information can be used to select 'your' John Livingston from others having the same name. Your John may not have filed for a pension, but it's the best way to answer that question!