Some good sources on the 13th New Jersey [my comments are in brackets] :
1. Letters of Dr. John James Hervey Love (1833-1897), New Jersey Historical Society, Newark (MG778). On June 19, 1863, Love wrote that three deserters were shot, two from the 46th Pennsylvania and one from the 13th New Jersey. On June 26, he wrote that the regiment crossed the Potomac at Edward's Ferry at daylight on that day. As of July 4, Surgeon Love was placed in charge of the First Division hospital, located at a large farm house about 2 1/2 miles from town, between the Baltimore Pike and the Taneytown Road. Love left the battlefield with the regiment at 4 p.m. on July 5. On July 9, he wrote that the 13th New Jersey had one killed and 23 wounded at Gettysburg, having gone into action with 307 men. On July 15, Surgeon Love wrote that he handled a captured Confederate standard with the names of 12 battles on it [from Brockenbrough's brigade?]. At the end of the month, he wrote that there were 14,046 Federal wounded at Gettysburg, and that 10,000 Confederate wounded were left behind.
2. Historical Sketch of Co. "D," 13th Regiment, N. J. Vols., compiled and printed for the use of its members by the authority of the "D" society (Newark, NJ, 1875). Company D, commanded by Capt. George A. Beardsley, was detached and sent to Two Taverns on the morning of July 3 as an escort to Confederate prisoners taken the day before, after which it returned to the front.
3. Samuel Toombs, Reminiscences of the War, Thirteenth Regiment New Jersey Volunteers (Orange, NJ: Printed at the Journal Office, 1878). An interesting regimental history. The 13th threw up breastworks of "old logs, stumps of trees, stones, etc." The 13th participated in a reconnaissance on July 4 [that took them past Latimer's Battalion] - "we passed a North Carolina battery, every horse of which had been killed, and judging from the dead around it, almost every man belonging to it must have met the same fate." Toombs wrote that all of the regiment's casualties during the battle were inflicted by enemy sharpshooters [perhaps all but one - see Duncan, below]. Toombs describes a typical scene on the march ... "As soon as the column starts upon the road, guns are slung across the shoulder and carried muzzle down, some are at 'right shoulder shift,' others carried across their left shoulder, while some men find relief by loosening the strap of the gun and throwing it across their bodies diagonally to the roll, composed of a piece of tent or blanket, which is worn over the right or left shoulder and brought across the breast under the arm on the opposite side. Some men have knapsacks, but most do not have that bulky and unserviceable structure."
4. Sebastian Cabot Duncan, Jr. (1840-1915) Papers, New Jersey Historical Society, Newark. Duncan, a member of Company E, wrote a lengthy letter to his father on July 8 about the fight. In a separate letter to his sister, Duncan wrote that John Van Winkle had received a slight wound at Gettysburg; he was struck on the wrist by a piece of shell. Another [Corporal Thomas H. Williams] in his company had received a musket ball in the knee; the leg was amputated. A third man in his company was shot through the hand. In a June 16 letter, Duncan identified the deserter in his regiment who was shot before the whole Corps - Christopher Krumber of Company B. Gen. Williams made a few remarks beforehand, and Chaplain Beck offered up a prayer for the condemned man.
5. Letter of Charles Augustus Hopkins (Captain, Co. K), Rutgers University Libraries, New Brunswick, NJ, Special Collections and Archives, (Ac 2167). On June 30, Hopkins wrote his father that the 13th was the first regiment in the Army of the Potomac to cross the Pennsylvania line. On July 4, Hopkins wrote that the regiment had three or four casualties on July 2 [the rest came on July 3], and that the men went 36 hours with nothing to eat, until that day.
6. Report of the Monument Committee of the Veteran Association of the 13th Regiment, New Jersey Volunteers, at the dedication exercises at Gettysburg, July 1, 1887, and the campfire on June 30. An interesting vignette is provided about John Kerschenkle of Company A, nicknamed "Hannes," [Hans?] which bears repeating here. "Hannes was one of the characters of the Regiment, as you well know, but he had a very poor handling of the Queen's English. Just across from Rock Creek, from the angle of our works, was a little house [Z. Tawney], gable end toward our line. Up in the gable end window of that house a number of rebel sharpshooters [from the 2nd Virginia most likely] had located themselves and had a complete enfilading fire on our works, and it was a very dangerous matter during the day to cross them. Company 'A' was nearest to the enemy and the moment we saw a head appear at the window of the house we all fired, but it was useless as they were so well protected. Hannes was a good soldier. He filled his pockets full of cartridges and crept down the slope until he got on the edge of Rock Creek, bringing himself within good range of the house. Hannes got down behind a big tree that was felled on the edge of the Creek, and the moment he would attempt to get up to shoot, the sharpshooter would get down behind the ledge of the window; when the sharpshooter would rise up Hannes would get down behind the tree; they kept this teeter-totter up for a long time. Finally, when Hannes came back, some of the boys says, 'Well, Hannes, how did you make it?' He replied, 'Vell, I told you, boys, I don't make it sometimes.' 'Well, what was the matter, Hannes?' 'Vell, I told you; I see the Johnnie, and the Johnnie he seed me; ven I jump up the Johnnie he jumped down, and ven I jumped down the Johnnie he jumped up. The Johnnie vas afraid of me and I vas afraid of the Johnnie.' "
7. Second Reunion, Veterans Association of the Thirteenth Regiment New Jersey Volunteers 1862-'65, Paterson, NJ, September 14, 1897 (Newark: Amzi Pierson & Co., 1898). June 30 ... broke camp shortly after daybreak, 3rd Brigade in advance, 13th New Jersey leading the brigade. ... leisurely (march) to Gettysburg. Farm houses had large casks filled with water [for the soldiers].