Grandma's Paternal Line

Randy's Saturday Night Challenge for April 9 was as follows:

Provide a list of your paternal grandmother's patrilineal line.  Answer these questions:

• What was your father's mother's maiden name?
• What was your father's mother's father's name?
• What is your father's mother's father's patrilineal line? That is, his father's father's father's ... back to the most distant male ancestor in that line?
• Can you identify male sibling(s) of your father's mother, and any living male descendants from those male sibling(s)? If so, you have a candidate to do a Y-DNA test on that patrilineal line. If not, you may have to find male siblings, and their descendants, of the next generation back, or even further.

So here's mine:

What was your father's mother's maiden name?  My paternal grandmother is Joan Garrison McMAHON, born 6 February 1927, died 1 March 1980.

What was your father's mother's father's name?  Joan's father was John Ward McMAHON, born 7 April 1902, died 24 June 1962.

What is your father's mother's father's patrilineal line? That is, his father's father's father's ... back to the most distant male ancestor in that line?

John's father was Timothy J McMAHON, born 14 May 1874, died 14 October 1939.

Timothy's father was Timothy McMAHON, born December 1845, died 29 March 1913.

Can you identify male sibling(s) of your father's mother, and any living male descendants from those male sibling(s)? If so, you have a candidate to do a Y-DNA test on that patrilineal line. If not, you may have to find male siblings, and their descendants, of the next generation back, or even further.

My grandmother's only sibling was a sister, so I've got nothing!!  Her dad's brother also had two daughters, so no males there either.  If I go back to Timothy's siblings, he had two brothers: one never married and had no children, the other had at least one son (I have no other info on this family at this time to know if there are any other males that may still be alive).  Would this even be of any help???  DNA research is not my forte.