Relative to the light artillery, the full regulation uniform was this one..., with the light artillery cap in lieu of a hat like the artillery. Also to be provided the common fatigue dress, including forage caps and flannel blouses...
During the war the light artillery caps were not often provided (from Kloster, US Army Headgear, vol. 2):
But were employed in a few wartime garrison settings in the South, like at wartime New Bern, NC and New Orleans, LA.
According to the veterans of Battery F, 1st Rhode Island Light Artillery, the volunteer light artillery were not "as a rule" provided with the full light artillery uniform, but their battery were so outfitted while serving with the garrison at New Bern, NC:
Here's an A.R. Waud sketch of Light Artillery in the regulation uniform, including the light artillery cap, at Richmond, immediately post-war. The light artillery cap had been so little used in the war time, that he referred to them as "new."
Since the army did not bother generally about the light artillery caps in the war, the light artillery units employed other headgear for uniform purposes. John D. Billings of the 10th Battery, Massachusetts Light Artillery, recorded that this was almost universally the government forage cap, adorned with the insignias intended for the light artillery cap or regulation hat:
At the light artillery camp of instruction Camp Berry the soldiers were to wear the forage cap as uniform:
Battery H, 1st Ohio Light Artillery, 1863;
Battery D, 1st NY Light Artillery, photographed on April 30, 1863 in camp: wearing third corps badges over the insignia on their forage caps...
Though in the field, many wearing slouch hats, etc. (or even the army hat worn slouch fashion) for comfort or convenience, as with Knap's PA Battery photographed on the Antietam battlefield in 1862.
Some artillerymen at Fort Rosecrans at Murfreesboro, TN, ca. 1864, one on the right in the regulation hat as a slouch hat, without insignias.
Battery B, 1st Illinois light Artillery, ca. 1864, with many of the men wearing uniform hats, largely slouch fashion by the looks of it...
Relative to the artillery regiments generally (or "heavy" artillery), they also appear to have largely employed the forage cap in lieu of the regulation uniform hat. Like the 1st CT Heavy Artillery, 1862, with forage caps, but otherwise in regulation full dress...
There were some artillery units which sported the full regulation uniform, but again principally in garrison setting. Like the 3rd Pennsylvania Heavy Artillery in garrison at Fort Monroe, VA in 1864 in full regulation artillery uniform of their branch, including hats:
The officers of the 3rd in the regulation artillery full dress....
Notice the Artillery officer's hats are looped on the right side, whereas the enlisted artillery men were to loop them on the left.
The General Staff hats to be looped on the right side:
A sketch of artillerymen in regulation uniform at Ft. Monroe guarding Jefferson Davis, in 1865.
There were occasions where the heavy artillery hat was employed as uniform for some light artillery units. For example, the 3rd New York Battery of light artillery, ca. 1861, outfitted with hats as regulation for foot artillery in camp. I notice they are looped either right or left side.
This battery also evidently had forage caps for fatigue dress...
Like the above example, Battery L, 2nd Illinois Light Artillery, with the Army of the Tennessee, was evidently provided with artillery hats in lieu of light artillery caps for uniform purposes in 1862-1863, besides their forage caps.