Was there ever a Kingsguard member that was sent to the Night's Watch for some reason?
King Jaehaerys I Targaryen accepted to let the turncloak Kingsguard members from King Maegor I Targaryen's Kingsguard join the Night's Watch under Princess Alysanne's guidance.
Five of Maegor’s Seven yet survived. Two of those, Ser Olyver Bracken and Ser Raymund Mallery, had played a part in the late king’s fall by turning their cloaks and going over to Jaehaerys, but the boy king observed rightly that in doing so they had broken their vows to defend the king’s life with their own. “I will have no oathbreakers at my court,” he proclaimed. All five Kingsguard were therefore sentenced to death…but at the urging of Princess Alysanne, it was agreed that they might be spared if they would exchange their white cloaks for black by joining the Night’s Watch. Four of the five accepted this clemency and departed for the Wall; along with Ser Olyver and Ser Raymund, the turncloaks, went Ser Jon Tollett and Ser Symond Crayne.
Fire & Blood, Prince into King: The Ascension of Jaehaerys I
There was also Ser Lucamore Strong who fathered a bunch of children and so was gelded and sent to the Wall.
"...Gwayne Corbray, Alyn Connington, the Demon of Darry, aye. You will have heard of Lucamore Strong as well."
"Ser Lucamore the Lusty?" Ser Loras seemed amused. "Three wives and thirty children, was it? They cut his cock off. Shall I sing the song for you, my lord?"
A Feast for Crows, Jaime II