Larry,
Do you know anything else about Gideon R. Barnes, like date of birth, brother's or father's names? What Texas county he was from?
I can't find any likely candidates for your Gideon R. Barnes in the units in Sibley's New Mexico campaign; however, there is a G. R. Barnes listed as a Corporal in Company C of the 9th Texas Infantry (Young's). This unit suffered a measles outbreak in January of 1862, by February this unit was across the Mississippi River. It's possible your ancestor may have become ill during this epidemic, was left behind due to illness and died after the departure of his unit. But, of course, this is all purely conjecture.
There is also a John Barnes listed as a member of this regiment and company. That's why I asked about relatives.
Company "C" of the 9th Texas was recruited in Grayson Co., TX.
Hope this helps and if you have any more info, please post it here.
Jim Martin