game of thrones - Are the Maesters on the Wall always members of the Night's Watch?

In the show we see that Maester Aemon is a member of the Night's Watch as well as being a Maester of the Citadel. I know his story line and why he took the oaths of both organizations. My question is whether the Maesters on the wall are always brothers or if they are just appointed by the Citadel?

Answer

George R. R. Martin has commented on this himself though it only explores the current maesters.

Maester Aemon is doubly sworn, to both Citadel and Night's Watch. That is true of the maesters at Eastwatch and the Shadow Tower as well.
_{So Spake Martin, SF, TARGARYENS, VALYRIA, SANSA, MARTELLS, AND MORE}

I have asked Elio and Linda this question on Twitter and although they can't confirm it they believe it was the case historically.

@westerosorg Hello, just a quick question. I know that the 3 current maesters of the Night's Watch are sworn to both orders but was this the case historically too? Thanks.
I can't say for sure, but I would be surprised if it was not the case that that was normal procedure.
_{Twitter, westerosorg}

This is also explained in the books.

That did not sound right to Jon, yet he said nothing. The maester was a hundred years old, and a high officer of the Night's Watch; it was not his place to contradict him.
_{A Game of Thrones, Jon VIII}

A toothless smile quivered on the ancient lips. "Only a maester of the Citadel, bound in service to Castle Black and the Night's Watch. In my order, we put aside our house names when we take our vows and don the collar." The old man touched the maester's chain that hung loosely around his thin, fleshless neck. "My father was Maekar, the First of his Name, and my brother Aegon reigned after him in my stead. My grandfather named me for Prince Aemon the Dragonknight, who was his uncle, or his father, depending on which tale you believe. Aemon, he called me …"
_ibid

Sam donned his blacks to say the words, though the afternoon was warm and muggy, with nary a breath of wind. "He was a good man," he began . . . but as soon as he had said the words he knew that they were wrong. "No. He was a great man. A maester of the Citadel, chained and sworn, and Sworn Brother of the Night's Watch, ever faithful. When he was born they named him for a hero who had died too young, but though he lived a long long time, his own life was no less heroic. No man was wiser, or gentler, or kinder. At the Wall, a dozen lords commander came and went during his years of service, but he was always there to counsel them. He counseled kings as well. He could have been a king himself, but when they offered him the crown he told them they should give it to his younger brother. How many men would do that?" Sam felt the tears welling in his eyes, and knew he could not go on much longer. "He was the blood of the dragon, but now his fire has gone out. He was Aemon Targaryen. And now his watch is ended."
_{A Feast for Crows, Samwell IV}

Although this only talks about the current maesters the wiki considers it to be the case historically too.

Maester's serving in the Night's Watch on the Wall are doubly sworn, and uphold both the maester's vows and the oaths of the Night's Watch.
_{A Wiki of Ice and Fire, Maesters}

This information could have come from The World of Ice and Fire which indicates that historical maesters of the Watch belonged to both orders.

The tales of long-dead rangers written down by maesters of the Watch all agree that the giants did not make homes or garments, and knew of no better tools or weapons than branches pulled from trees.
_{The World of Ice and Fire, Ancient History: The Dawn Age}

Note that the only three maesters we know of for the Night's Watch are Aemon (Castle Black), Mullin (Shadow Tower) and Harmune (Eastwatch) all of which are depicted as being members of the Watch. The only other example is Samwell Tarly who is again a member of the Watch though he is a member before becoming a maester. It's unclear if the others were maesters or brothers first.