You might ask for a Census lookup by Clarissa, the volunteer listed on this page: http://www.rootsweb.ancestry.com/~okwagone/lookups.html
Perhaps she might have some information on Jackson Switch as well.
I'm finding Tom as Thomason Cox in the 1920 Census, and it says he was born 1864 or 1866. This is the only census record where I'm finding him (so far) with a wife named Rhoda.
If your Thomas Milton Cox was indeed born circa 1883, is it possible Thomas had a brother named Al, and that they were both single and living in the same household in 1910?:
1910 United States Federal Census
about Tom Cox
Name: Tom Cox
Age in 1910: 27
Estimated Birth Year: abt 1883
Birthplace: Illinois
Relation to Head of House: Head
Father's Birth Place: Illinois
Mother's Birth Place: Kentucky
Home in 1910: Woodbury, Cumberland, Illinois
Marital Status: Single
Race: White
Gender: Male
Household Members: Name Age
Tom Cox 27
Al Cox 25
Now that I've finally found your tree on Ancestry, I see you have his birth as 1866.
I hope this helps.
Edit-
Thanks for clarifying the birth year, as you know it helps significantly to narrow down the search. I've been looking through the 1910 census and your tree, which states you think they may have left Missouri around 1900 for the OK land rush, and am simply not finding Thomas (or T M or Tommy or Tom or Thomason), or Rhoda, or Arthur in the 1910 census in any state. It looks like you expect them to be in Oklahoma in 1910, since they left for OK and were still there in 1920... still looking...
Edit-
Have you been to the Bureau of Land Management site? There was a Thomas Cox who got a land patent on 1/6/1910 in Tillman County, OK (link to search page in Source box below). It could be the right Thomas, which might mean he and/or his family was/were in Tillman county in 1910.
Final edit-
Now back to your original question about Jackson Switch: I wondered if they lived in the country and the switch was an old railroad switch. Then I found this on an old forum post, it sounds like the same Jackson Switch you're looking for:
"Subject: [JACKSON] Jackson Switch n. of Coweta, OK or Indian Territory?
Date: Thu, 22 Jun 2000 08:26:40 -0500
Dear Oklahoma Shahans & Jackson Connections -
As we left the Shahan Reunion in Coweta a few weekends ago, we were
driving North on highway 51, out of Coweta, and then turned West perhaps
still on "Old Highway 51"... there was a jumble of railroad tracks there, perhaps an X... and Bryan said "this was called The Jackson
Switch" - I don't know where he got that - perhaps as a child from his father, or perhaps it was labeled that way at one time? Beverly,
again, can you confirm this? Karla"