[@RyoRyoRyoken]The latter. It keeps Yurei mostly docile and contained, though he can briefly gain control at times if Shizuka is agitated or under a lot of stress. Yūrei is a facet of Shizuka that was formed during him seeing his father get killed. His mind fractured, and all the anger and frustration that he'd been containing(both the murderous kind and the everyday anger and frustration that he kept locked up on a daily basis) formed into a separate personality.

 He's tied to rage and anger, and only triggers when Shizuka loses control of his emotions, which happens whenever the eyepatch is removed. It'skinda like his version of a security blanket, and he gets super paranoiud and agitated without it, which often leads to Yūrei's release most of the time, and quickly.

Edit: Will get to Buddha's stuff when I'm off work.