Gloria, that newspaper article I mentioned earlier in the string from The St Louis Republic Newspaper 11/12/1893 pg 18 reprint included this about his execution and burial..
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The prisoner was taken outside of the city limits near the present residence of Mrs. Rush Owen

The body of the dead "Spy" was buried near the place of execution where it remained until the opening of the Confederate Cemetery four miles south of Springfield. The remains of Lieutenant Brownlee now rest with the ashes of kindred in arms and receive each returning spring a floral tribute from sympathetic hands.
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Gay