The T and P is identified as the Texas and Pacific Line in Norm Cohen, "The Long Steel Rail."
Cohen lists it with the same skeletal information posted above.

The railroad song, "Only a Brakeman," includes a verse (in one version) that mentions the Texas and Pacific, but it is not related to the song of this thread.

Only a brakeman gone on before,
Only a brakeman we'll never see no more,
He was doin' his duty on the old Tee Pee train,
But now he is sleepin' on the old state plain.

Vance Randolph, Ozark Folksongs, vol. 4, "Only a Brakeman," coll. 1927, with musical score (complete song).