EDIT: Now that I have a little bit more time to spend on this, there's more, and better, info.

This previous answer by a deleted user to a similar question, I think, addresses part of your question. The TL;DR is, there were only twelve living Revolution veterans by 1864 receiving pension for their service, and all that is known of their thoughts on the Civil War is included in that book The Last Men of the Revolution.

On October 19, 1863, the New York Herald published an article about them. And then on June 14, 1864, the New York Times published a similar article. The Herald article was subsequently published as a pamphlet. Between the two articles, it can be gathered that, as of March 4, 1861, there were likely less than 30 veterans still living.

Of them, twelve were still alive in loyal states as of 1864 - there were probably several more still alive in early 1861. And then those living in disloyal states, at least six were still alive in early 1861, and as many as nine, but probably no more than that.

One of the twelve known survivors as of 1864 living in a loyal state had served a seceding state during the Revolution (James Barham of Virginia), but had moved to Missouri at some earlier point. The author of the book The Last Men of the Revolution, Elias Brewster (under the pseudonym E.B. Hillard), attempted to track Barham down in 1864, but could not get in contact with him:

"Endeavor has been made to find him and procure his photograph and a sketch of his life, but thus far without success. As no intelligence, however, has been received at the Pension Office of his death, the hope may be indulged that he is still living."

So, Brewster settled on interviewing the six living vets in Union states who were well enough to be interviewed. That previous AskHistorians answer summarizes what they had to say.

The Herald article gives the names of all the men from seceding states whose Revolutionary War pensions had not yet been reported cancelled as of March 4, 1861. The Herald correctly notes that, by the time their October 1863 article was written, several of them would have died, but the pension offices from the seceded states had stopped reporting anything to the U.S. federal government in early 1861, so the status of these Southern veterans was unknown.

But with subsequent research, we know the status of at least 9 of these 12 Southern veterans.

The three whose status I could not track down are:

• John Brooks (North Carolina, born 1757-58)

• Henry Willoughby (Virginia, born 1759)

• James Copeland (South Carolina, born 1764)

Of these three, it's a safe bet that John Brooks did not survive past 1862, given where he lived. According to the book Driven from Home: North Carolina's Civil War Refugee Crisis, in the summer of 1862, there was a yellow fever epidemic in the area of North Carolina where he lived, which has been estimated to have killed 10% of the population. Many North Carolinians fled the area (carrying the epidemic with them), and many Unionists had already fled. Given Brooks' age, it's very likely he did not survive past that summer, if he was even alive at all at the start of the war. By 1862, he was somewhere between the ages of 103-105, and medicine being what it was, it's doubtful he could have easily left his home, or survived the epidemic, though it's still a possibility.

More is known about the fate of the other nine. Three of them had already died before 1861, and their fate hadn't yet been reported to the pension office by the time Lincoln was inaugurated:

• Reuben Stevens (North Carolina, born 1762, purportedly died 1860 according to his headstone)

• Israel McBee (Virginia, born 1761, purportedly died 8 September 1860, though his headstone says 1861)

• John Hames (Virginia, born 1752, purportedly died 9 October 1860, with that year on his headstone)

Of the other six, five did live into the war for some period, though there is no record of what they thought of the war as far as I have been able to find. The youngest of these men died at the age of 99. The oldest died at the age of 106-107. Only one of them (Peter Bashaw) would have been alive at the time Brewster wrote his book in 1864, and there's no guarantee he would have been in good enough health to answer any questions:

• William Coggin (South Carolina, born 1755, died 1862 according to his headstone)

• Roland Ware (North Carolina, born 1759, purportedly died 22 Mar 1863, though his headstone says "Spring 1864")

• Micajah Brooks (North Carolina, purportedly born 25 Dec 1761 and died 15 June 1863, according to an article in the April 1978 issue of Northwest Georgia Historical & Genealogical Society Quarterly)

• George Roberts (North Carolina, born 1758 and purportedly died 1 Jan 1864, according to a 1923 letter by one of his descendants sent to that descendant's representative in the U.S. House, and collected in Roberts' pension file held by the National Archives - you can find it paywalled at Ancestry.com)

• Peter Bashaw (Virginia, purportedly born 31 Mar 1763 and died 20 May 1864, according to his headstone)

Again, of these five men, there appears to be no record of their thoughts on the war, if they even had any at all, given their age.

That just leaves one more Southern veteran reported on by either the Herald or the Times. His name was Matthew Seay. He was born in Virginia in 1763, according to the Herald article, and he died just before July 21, 1861. We know the latter date because his death was reported in the Richmond Dispatch newspaper on that date. And the brief article gives the only account of any Revolutionary War veteran's thoughts on the Civil War, when that vet was still living in a seceding state. However, it should certainly be taken with a grain of salt. This was likely just a bit of propaganda. Given his age of about 101 or 102 (the Dispatch said he was 104) and given his death less than two months after Virginia seceded and about three months after Fort Sumter, it's unknown if he actually was mentally aware of what was going on. The Dispatch, or a Confederate family member, very well may have invented what was attributed to him. Then again, the threat of secession and war had been going on for some time, so it's entirely possible these are a fair characterization of his own thoughts. So, it's the most we have from a Southerner living in the South, though not exactly from a neutral source. Here is the text of the Dispatch article in full:

"ANOTHER VETERAN GONE.—Mattew Seay, one of the few remaining veterans of the Revolution, departed this life a few days since, at his residence in Henry county, at the advanced age of one hundred and four years. It is said that the old warrior was so much exercised over the present war and his inability to engage in a second struggle for Freedom, that a general prostration of his system was the result. Quietly and calmly he breathed his last, with a blessing upon the Southern forces in the field. He had gone to the manes of the patriotic dead."

There are a few more veterans that neither the Herald, the Times, nor Brewster tracked down in 1863-64, because none was receiving a pension (and all would have trouble proving their service to the pension office). One of them was John Gray, born in 1764, who was granted a pension by a special act of U.S. Congress. He served Virginia during the Revolution, but had moved to Ohio around 1800. He is the only other "Confederate" whose thoughts were recorded, though he'd been living in the North for over a half century by the time the war broke out. A book of his purported memoirs was published in 1868. According to these memoirs, he was a Unionist:

"His want of property excluded him from voting in Virginia for his beloved Washington. And he often said, had it not been for that, he might have lived and died in Virginia. But he was a Republican at heart, and could not well get over the insult thus levelled by aristocratic distinctions against his proud manhood. Saving this, John Gray was a true lover of Virginia. He often mourned and even wept over Virginia's wayward course in the Rebellion — for John Gray was loyal; but when the war was over all his feeling against Virginia left him."

cont'd...