Step 1: Killian's dehiscence is a triangular gap of weakness in the posterior pharyngeal wall musculature.
Step 2: It sits between the two heads of the inferior constrictor: the obliquely running thyropharyngeus above and the transversely running cricopharyngeus below. This location corresponds to the cricopharynx.
Step 3: Because muscle support is deficient here, the mucosa can balloon out to produce a pharyngeal pouch, and instruments can perforate the wall at this point during endoscopy.
Step 4: Distractors such as oropharynx, nasopharynx and vocal cords do not house this gap, so they are ruled out.
\[\boxed{\text{Cricopharynx}}\]