Looked thru the Time-Life book, “Gettysburg.” I believe the painting you referenced appears on pages 94-95. The title is “Rothermel’s painting of the Confederate attack on Culp’s Hill on the morning of July 3 accurately shows the 1st Marland’s mascot (right, background) out ahead of the charging regiment. The Federal defenders (foreground and right) repulsed the attack; the dog was killed, along with 31 men of the 1st Maryland.”
Interestingly, John Wesley Culp was killed the same day on Culp’s Hill. A native of Gettysburg, as a child Wesley Culp played on the hill which was owned by and named for his uncle, Henry Culp. When Wesley became a teenager, he took a job with harness company that manufactured leather harnesses for carriages and wagons. When the owner of the company moved his business from Gettysburg to Shepherdstown, VA, in 1858, Wesley moved with him. He made many new friends there and, when the war broke out in 1861, he enlisted with his new friends in the 2d VA Infantry, which was part of the attacking force on Culp’s Hill. Sometime during the fighting Wesley was shot and killed. Wesley was buried and his grave supposedly marked by his fellow soldiers of the 2nd Virginia, though the only remains of him ever found was a rifle stock with his named carved into it. His body was never identified and recovered.
In an interesting twist of fate, Wesley was carrying a message to be given to another Gettysburg native, Virginia "Jennie" Wade, who was also the only civilian killed during the fighting in Gettysburg. She was shot by a stray bullet while she was baking bread in her kitchen.
Wesley's brother William Culp enlisted in the 87th Pennsylvania Infantry and survived the war.