Of course, it should count, but we should get one question credit because the Elendil’s Heir asked a question back
Nice try. 
Was he a US President?
- No
- Was he in Congress?
- Yes
Was he in Congess later than 1960?
- No
A 20th Century American man who was in Congress some time before 1960, was not a US President, held an executive office at some level of government at some point, who died before 1989… hhmmm… maybe we can make a list of people who fit that criteria then narrow it down.
First elected to Congress in or after 1930?
- No
A 20th Century American man who was first elected to Congress before 1930, was out of Congress before 1960, was not a US President, held an executive office at some level of government at some point, and died before 1989
If I got everything correct thus far, we are looking for US Representative or Senator that was first elected to a National office between the years 1900 - 1930. Who never became President.
Has this guy ever run for President or Vice President?
- Yes
Excellent!
Not my guess, but Charles Fairbanks seems to fit:
Senate: 1897-1909
VP to Teddy Roosevelt: 1905-1909
Died: 1918
Not my guess, but William Jennings Bryan seems to fit:
House: 1891-1895
Secretary of State: 1913-1915
Died: 1925
Ran for Prez: 1896, 1900, 1908
To make up for the Pee Wee Herman question, I’ll tell you… it’s neither of those guys. Although I once did a college research project on Bryan’s service as Wilson’s Secretary of State, which I found an interesting topic.
Since this is question 20, I got to get specific.
Is it John Nance Garner?
My first thought was William Jennings Bryan as well. But I ruled him out because he started doing noteworthy things in the 19th century. running for prez at age 36 was one of them.
Thanks for the tip. 
Not my guess, but James Sherman seems to fit:
VP under Taft: 1909-1912
House: 1887-1891, 1983-1909
Died: 1912
Mayor of Utica, NY: 1894