This seems to be the same song ClaireBear posted a link to, but it's not from the Civil War era. From Indiana University Sheet Music Collections:

JUST AS THE SUN WENT DOWN
Lyn Udall
New York: M. Witmark & Sons, 1898.

1. After the din of the battle's roar, just at the close of day,
Wounded and bleeding upon the field, two dying soldiers lay.
One held a ringlet of thin gray hair, one held a lock of brown,
Bidding each other a last farewell, just as the sun went down.

CHORUS: One thought of mother, at home alone, feeble and old and gray;
One of the sweetheart he left in town, happy and young and gay.
One kissed a ringlet of thin gray hair, one kissed a lock of brown,
Bidding farewell to the Stars and Stripes, just as the sun went down.

2. One knew the joy of a mother's love, one of a sweetheart fair
Thinking of home, they lay side by side, breathing a farewell pray'r;
One for his mother so old and gray, one for his love in town;
They closed their eyes to the earth and skies, just as the sun went down.