Well, you already noted I'm sure that Harmon had a son Henry born in 1812. Unfortunately, I know precious little about him, so I can neither confirm nor deny your link to this tree. Let me just say that for the most part it seems that when given a choice, this branch prefered to spell their name with an "a" for Fahringer or Farringer, and only when someone else spelt their name did they get other versions like Forringer or Ferringer, so your guy may be from one of the other branches. But who knows....
I have done a little searching and found Henry Farringers in the US. Pennsylvania census. Here's what I found (via Ancestry.com):
Henry Farringer 1840 census Armstrong county, Red Bank twp. Henry Fahringer 1850 census Montour County, Roaring Creek twp. (This is most likely Harmon's son as this was the same Co. and Twp. that Harmon lived in.) Henry Farringer 1840 census Jefferson county, Porter twp.
These are just a few. I believe I only looked for Fahringers and Farringers, but not Ferringers, so your guy may be out there, too. (Unfortunately census info on Ancestry is info you must pay for, though occasionally they have free trial periods, which is how I got my info. Or if you aren't as cheap as me, you could actually pay! They do have a lot of valuable info.)
Hope this helps. Let me know if you do connect to this tree. I will keep you updated as I try to find out more info on Harmon's ancestors.