And hey, I have L.o.t.H.T. episodes on iTunes. When I watched Shawn enter the Spider's Lair with the horseshoe, what was actually swinging was a rope from the room's rope web, not the half pendant. Therefore, the half pendant was hanging on the Golden Idols-Shrine actuator. Also, I'm not new to Phantom's Temple, FYI.
Sorry, I saw that you had a post count of 2, so I assumed that you were new.
However, I'm still thinking that the object that I circled is the half-pendant due to its geometry (thickness and shape) and color. There is something there in that screenshot that is the same color and geometry as the hidden half-pendants that we've seen previously. Also its color is a rustic color, unlike the pure white of that segment of rope that you've referenced.
Also, during the temple run itself we get a clear look at the Idols-Shrine actuator, and there's nothing hanging from it:

My guess is that the Spider's Lair was a double-whammy (Temple Guard & Dead-End room), and that the run was set up like the run from the "Lost Logbooks of Magellan". (There WAS a guard in the Spider's Lair, seen while Shawn was exiting the room) The producers banked on the fact that if the team tried the direct path (ala Shaka Zulu) they would've run into the half-pendant on the opposite side of the room before having to retreat back to the Throne Room to go up. Then Shawn would've had to go into the Spider's Lair, get the half-pendant, then take over at the Heart Room where Lucretia would have been taken out.