So, just returned from a trip to eastern Europe and am anxious to continue my search.
I found the following Junkins listed online under Griffiths Valuation: Ballyscullion Grange Parish 1861 and 1862 …
Junkin, Alexander L: Gillistown
Junkin, Andrew L: Gillistown
Junkin, James L: Ardnaglass
Junkin, John L: Mill Quarter
Junkin, Joseph L: Gillistown
Junkin, Mary L: Ardnaglass
Junkin, Robert L: Gillistown
… Have learned that Ardnaglass and Gillistown are neighboring townlands. So, I assume Andrew may be the person who erected the gravestone to his parents (inscription provided in an earlier post).
Muddling my efforts slightly is that I have discovered an Andrew Junkins, shown on the 1880 US federal census as living a few doors from my great, great uncle Hugh Leake (brother of my great grandmother, Mary (Leake) Junkin) in Hokendaqua, Pennnsylvania, USA, and appearing directly behind him in an 1888 picture from the Thomas Iron Works, also in "Hokey". Is this the same Andrew Junkin/Junkins? Further leading me to believe there is a connection is that my grandfather was named Andrew Junkin and there seems to be a lot of honoring of fathers and brothers among naming conventions in the family.
I'm sure upon re-reading this post, it will be a confusing mess, but as I said, I do wish to take up the chase. Thanks very much to all who have already helped!