The Forlorn Watchman
Although you might have stumbled onto the quest locations, the quest itself won't activate except by following up on rumors in Bravil or unless you happen to speak to the Forlorn Watchman when he is at the end of his nightly walk near Fort Irony (a small, one-level Goblin lair).
The quest locations themselves are easy enough to find. Bawnwatch Camp is on a little island a bit south of Bravil, just outside of the Ayleid ruin, Bawn (a three-level undead lair). The island connects to the mainland by a short bridge, but it does not connect to the main road. The Mouth of the Panther is very close to the bridge where the main road crosses the Panther River on the east side of the Niben. You might have even explored the Emma May when you came across it. Even if you have stumbled across both locations, there is nothing related to the quest that you can do until it is active.
The Watchman appears at Bawnwatch Camp every night at 8:00 p.m. After appearing, he walks to a position a bit south of Fort Irony, across from the where the Panther River empties into the Niben. It is possible to run into him by chance, but since he is only available at a certain time, it's not likely. He has nothing to say before and during his walk, but if you try talking to him, your Journal will suggest following him to see what he does. He will force a conversation at his destination when you're close enough.
The more common route is to follow up on rumors about the Watchman in Bravil. When you do so, you'll be pointed to Gilgondorin, the proprietor of Silverhome-on-the-Water. The inn is just inside Bravil's gate. When you speak to Gilgondorin about the Watchman, he'll give you all of the information you need to get started and mark Bawnwatch Camp on your map.
When you decide to follow up on the quest, proceed to Bawnwatch Camp and wait until 8 p.m. When the Watchman appears, follow him until he stops and speaks to you. He tells you that his name was Grantham Blakeley, that you'll find him in the Mouth of the Panther and that he wants to be released. Sounds like a plan.
When you get to the Mouth of the Panther, you'll find the wreck of the Emma May, a ship, on the south side of the river. Although you can reach the top deck of the ship with a good enough Acrobatics skill, there is no entrance there. Instead, the entrance is through the hole in the side of the ship. If your Stealth skill is good, you might be able to get in safely. But the odds are pretty good that you'll be spotted as soon as you enter, so be prepared to come in swinging.
The ship is haunted, so you'll need to be able to deal with spooks. These are leveled spirits ranging from Ghosts up to Gloom Wraiths on each deck: two on the upper deck (one on each side of where you enter), two on the mid-deck and one in the Captain's Cabin. It is not necessary to visit the Captain's cabin and the loot is hardly worth the bother, but it's there if you want to check it. Although it's not necessary, you'll want to read the ship's log while you're on the upper deck to get the story of what happened.
On the bottom deck there is only one creature: the ghost of Gable the Traitor. He's a Gloom Wraith with a really cheap curse spell, so be prepared to do a little attribute restoring after you're done. Gable only has one item in his inventory: a key that opens the locked door behind him and the shackles on Blakeley's skeleton in the room behind the door.
Once you release Blakeley, the Watchman will appear and thank you. After his little speech, you'll find a map on the floor behind the pole where his skeleton was chained. The map points to a treasure chest in the river, a couple of bends to the east. So hightail it over there. You'll probably need to deal with a couple of random critters on the way and, depending on your progress in the Main Quest, you might have an Oblivion Gate and its attendant critters near the shipwreck. Blakeley's treasure is in a chest wedged between some rocks in a fairly deep part of the river, just a little south of the small pier. The loot is all random, but you've got a shot at gold, gems, jewelry, a soul gem and an enchanted weapon.