Re: Elmer Dawson Cooke, b. 1864 or 1865 in Ohio, son of Capt. Joseph K. Cooke
Here's a little info that might point you in the right direction (if you don't have it already):
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06/05/1917 World War I Draft Registration - Oklahoma - Ottawa County
COOKE, Elmer Frank, born 02/03/1891 in Kansas.
Living in Picken, Oklahoma.
Working as a Miner.
Single, supporting his mother and invalid sister.
(Half Ottawa Indian?)
1920 Federal Census - Oklahoma - Ottawa County
Appears to be the same man, working as a Lead and Zinc Miner.
With wife, stepdaughter, daughter.
The name is garbled--indexed as (Trevor or Frank) COX, but close inspection sure looks like Frank COOKE.