I know just a little more about him. Since I posted that cemetery list, I have found two more Rigsbys in that Muskogee cemetery: Mabel E, and Ethel M Rigsby Andrews, apparently their daughter.
But I haven't figured out who he is yet. I can eliminate all the Homers and Harolds in my database except a Homer L born 1899 AL, who is not a very good match.
He is on the 1930 census in Creek Co OK with his wife's parents Jess? and Bell Hall. It says he was born in OK, but doesn't give his parents' birthplaces.
On the 1920 census he is in Okfuskee Co OK in a household of Alonzo Orrell and wife Ellen, listed as a nephew. His parents are shown born VA/AR. I don't know of a Rigsby marrying an Orrell, and the only Rigsby born in VA who was in AR before 1900 was a John who died before 1860.
I can't find him anywhere on the 1910 census. There are several Homers and Harolds listed, but I can identify them all. Alonzo Orrell is in Muskogee Co OK, but Homer is not with him. But, going off what you said about Charles Potts, I found this entry in Muskogee Co:
Charles V? Potts 36 AR/GA/TN mother Anges Potts TN/SC/VA niece Homer Jack 12 OK/blank/AR niece Lola Jack 11 OK/blank/AR
The name and age match, but I have no idea where the last name Jack would have come from. If that entry matches what you know of Charles Potts, it must be Homer Rigsby, and it looks like he had a sister Lola.
Unfortunately, there just isn't a match anywhere in OK or Indian Territory on the 1900 census. There aren't that many Rigsbys there anyway, and no Homer or Harold or anything close. The only family with children the right ages has a James age 2 and Jessie age 1, but that family is in Sequoyah Co on the 1910 census with both children. I don't see a match in AR either. My only guess is that his family wasn't enumerated.
That's all I can tell you about him, I'm afraid. If I ever do find out who his parents were, I'll post it as a correction to the cemetery list.