There were 43 deserters among the regulars in Texas in January, 1861. Then 319 deserters from the regular units in Texas occurred from January to April, 1861 during the secession crisis according to Mr. Weinert's history of the Confederate Regular Army, (the book) p. 26. These desertions were principally prior to the commencement of the war in mid-April apparently.
For example, of about 100 privates who deserted the 2nd US Cavalry (later 5th Cavalry) in Texas in the spring of 1861, they deserted before the regiment marched out of Texas in February-March, 1861:
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And before the commencement of the war...
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The commencement of the war was on April 12, according to the USA, the President noting:
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President Lincoln noted in July, 1861 that since that commencement of the "hour of trial" (particularly April 12) to that time there were no "
known" desertions to the enemy by Regular Army enlisted men.
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But there were some.
A soldier recording their capture and imprisonment in Texas as Prisoners of War from the commencement of the war noted later that a few of the 8th's men deserted specifically to join the Confederates during July-August, 1861...
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From April 1861 to March 1865, the Government recorded 5 officers and 1,274 enlisted men deserted from the Regular Army nation wide. How many from among the POWs in Texas is apparently not been exactly calculated.
Martin Hardwick's "Confederate Army in New Mexico" (1978) has some Confederate rosters with notices of some of the men who had deserted from the US service among them; deserted either before or after the commencement of the war.
Someone would have to go through the Regular Army enlistment register, which gives the final disposition of each man to get the whole number, and compare notices of desertions in Texas in 1861 with the surviving Confederate records.
The troops surrendered by General Twiggs in March, 1861 were not POW prisoners of war. The deserters were just classed as deserters. Only those in Texas from the commencement of the war in April were held as POWs, and Van Dorn was ordered to attempt to recruit them to desert the US Army and join the Confederate Army:
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The number who did so was reported to be small.
Where General Van Dorn subsequently reported from San Antonio in June, 1861 that he had mustered into service the company of "old soldiers" under Captain Edgar, which is that which served with McCulloch's command... and sent a similar company of "old soldiers" to Fort Bliss, it might not regard specifically deserters. The report quoted by Weinert read:
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Mr. Wienert (p. 26 of his book) presumes this is a reference to US Army deserters, and that these units might have been part of the Confederate Regular Army. But these were not Confederate Regular Army units. The C.S. Regular Army enlisted men in the Confederate service (the few there were of them during the war), as in the USA, individually and not mustered in as volunteers.
Captain Edgar's Artillery Company was originally the "Alamo City Guards" of San Antonio, which entered Texas State service before the war. And after being mustered into Confederate Army service, was in the "Provisional" CS Army:
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And while it is possible some US Army Deserters of '61 were among them, many of the "Old soldiers" mentioned were likely men recruited from among the population of US Army veterans resident in Texas. As of 1860 this class comprised a large number.
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So numbers of the citizens in Texas, including San Antonio, many of whom abided the secession/Confederate authorities were
discharged "old soldiers"...
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Regarding the US Army
Deserters of '61, the Confederates found them to be just such hard bargains for the most part apparently, as the 8th Infantry chap previously quoted presumed. They were not in the regular CSA service, but the Provisional Army with the 3rd Texas Volunteers with Captain Buquor's and Captain Marmion's companies...
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Captain Buquor's company was mustered into Confederate Army service on May 25, 1861, and served as Company A, 3rd Texas Volunteer Infantry, CSA.
Captain Marmion's company of artillery from Bexar County was mustered into Confederate Army service September 18, 1861, and was in 1862 reorganized as Company G, 3rd Texas Volunteer Infantry, CSA.