According to Mary Livermore, in her My Story of the War, at the beginning of the war, Union women also got busy making havelocks. Here's part of her account:
"Our men, of course, must be equipped with this protection, and forthwith inexperienced women, and equally inexperienced men in the army, gave orders for the manufacture of Havelocks. What a furore there was over them! Women who could not attend the "sewing meeting" where the "Havelocks" were being manufactured, ordered the work sent to their homes, and ran the sewing-machines day and night till the nondescript headgear was completed. "Havelocks" were turned out by thousands, of all patterns and sizes, and of every conceivable material.
". . . While the Havelock fever was at its height, the Nineteenth Illinois. . .was mustered in, and was ordered to rendezvous at Camp Douglas. A detachment of the "cake and pie brigade," as the rollicking fellows called them, paid the regiment an early visit and were received by the men who were not under drill, en Havelock. As the sturdy fellows emerged from their tents, all wearing "the white nightcaps," as they had irreverently christened the ugly head-dress, their appearance was so ludicrous that a shout went up from officers, soldiers, and lady visitors. They were worn in every imaginable fashion,-- as nightcaps, turbans, sunbonnets, bandages, sunshades,--and the fate of the "Havelock" was sealed. No more time nor money was wasted in their useless manufacture."
The Havelock craze surely did effect the development of the Havelock Hat. The Havelock Hat did provide shade for the rear of the neck. I think the issue with the Havelock Hats was that people found them lacking in smartness. Despite how practical or unpractical they might be, one only needs to look at period photos of them to see how ugly they looked.
In another thread we are discussing caps and I have always wondered why these Whipple hats are not call Whipple caps. They are often called Whipple hat/Havelock. Earlier I said I did not remember the Southern term for the Whipple cap worn by Southerners, now I remember that Southerners called them Excelsior hat/caps.
Both the North ans South used but the Whipple type Havelock hats used by the Southern soldiers were called Excelsior hats. The name change did not have a real impact on how well the Confederate troops would have liked the Havelock hats.