Sometimes, after Merlin had used some blatantly obvious excuse to cover up times he was missing, (saving Arthur's royal backside) and sometimes when Arthur was just more annoyed than usual, he would send Merlin to go clean the unused chambers in the castle. To which Merlin would roll his eyes, and remind himself that it was all for the good of Camelot. And more times than not, when Gwen wasn't busy, she'd join him, making the mundane tasks more bearable.
So as the pair scrubbed floors, polished silver, folded blankets, and aired out rooms, they's sing. Most of the songs were just simple little tunes that they'd heard at harvest celebrations throughout their childhoods, but Gwen had picked up some lovely pieces from her time at the castle, and Merlin had been taught a few traditional songs from the druids, and they'd teach each other the words.
Unbeknownst to them, their singing didn't go unnoticed. Their voices echoed down the stone hallways to the ears of bored guards or passing servants. The floating harmonies of Gwen's rich alto and Merlin's clear tenor would distort as they echoed, making it difficult to make out individual words. As the sound traveled through empty corridors and twisting hallways, warping the sound until you couldn't tell where it was coming from or what was making it. When a curious servant looked to discover where it was coming from, all he'd found was Merlin and Gwen, who denied hearing anything at all.
Well that servant told another, when asked where he'd run off to, and then that one told his sister that night about the mysterious singing heard in the castle. The sister, a seamstress, always listening for fresh gossip told the girls at the shop, who all agreed that is must be a ghost. One of the girls asked the guard courting her if he'd ever ran into the ghost on the upper floors of the castle, and he warned the other guards, who all confirmed that they too had heard something.
A visiting noble overheard a conversation between two guards who gave the empty chambers a wide berth, who mentioned it to Arthur during a hunting trip. Several of the knights accompanying them had heard of the ghost too. And to Merlin's credit, he did a very good job of keeping a straight face at the mention of the "ghost", though when he shared the news with Gwen, it was a while before they stopped laughing.