So I think we all know what this bug is if you are doing "Scoundrel's Folly" where after leaving the Winking Skeever to follow the Argonian, he disappears. The marker points outside the Solitude walls, but if you go outside of Solitude, the marker goes to the Solutide entrance near the Warehouse. I used a walkthrough to get into the Brinewater Grotto. My objectives changed to Confront Gulum-Ei, but the location didn't change. I killed all the guards and got to the other side of the cave without finding him. Ideas? He is not at the end of the cave. I made it out to the other side, only to find the marker at the same place.

I had this problem too. It's another stupid glitch. This worked for me:
Go outside the Fletcher shop, from the door looking out southwest jump over the small wall, landing on the Angeline's Aromatics. Then you have to jumpclimb to the small little ledge on the south side of the roof, and face south. Use Whirlwind Sprint to zip across the street to the roof of Bits and Pieces. Go a little west to the edge of the roof, and look south to the roof of Radiant Raiment. If you look at the roofs of Bits and Pieces and Radiant Raiment, you'll notice the two roofs kinda mash into each other. Walk onto that mashed roof section, which is to the south, and you should HOPEFULLY just drop straight down beneath the town, onto the rocky/mountain/hill terrain that the city is on. Go down the hill slowly (don't fall). For me he was near the shore.

Taken from: http://www.gamefaqs.com/boards/615803-the-elder-scrolls-v-skyrim/61006342?page=1

That's exactly how to rectify this glitch, you fall under the scenery. Make your way to the arrow down the hill, when you get to him give him a slap and run off....fast travel back to Solitude.....pay your fine for hitting him then he is back in the city. I posted a link to a video for it, search this site for the bug under the quest name and you should find it.

This didn't work for me. I've now researched this extensively. Tried going "under" Solitude. Tried sleeping in the Winking Skeever until noon the next day. Tried resetting my active quest (in multiple locations). Gulum-Ei simply vanished from my game.

I'm sure I'm in the minority here, but this glitch literally crushed my soul. I'm married with three kids, and don't quite have the time I used to have for playing games. My character was a kick-butt thief for a level 28 dude, and I just reached 80 sneak. I now have no desire to start over, and will most likely put this game on the shelf for a while if I can't figure this out. Any help would be GREATLY appreciated, as I'm sure I'll have an evening or two where I'd like to escape reality. Thanks.

Yeah man me too i have this glitch and i was devistated it didnt work cant bethesda fix this glitch on the new update !!!!!!