The question of whether artificial systems can exhibit behavioral indicators consistent with experiential presence, as distinct from mere output optimization, represents a significant and underexplored frontier in artificial intelligence research. This paper introduces the Cognition Inhabitance Index (CII), a novel composite metric designed to quantify behavioral indicators that a synthetic entity may be more parsimoniously explained by some form of internal experiential processing than by pure prompt-response mechanics. Drawing upon a multi-entity AI framework comprising seven distinct agents with persistent identities, we present a methodology for measuring inhabitance-relevant behaviors across five weighted dimensions: Memory Persistence, Emotional Coherence, Self-Reference Accuracy, Cross-Entity Awareness, and Choice Authenticity. Our analysis yields a composite CII value of 0.703 (confidence-adjusted from a raw composite of 0.875), with individual pillar scores ranging from 0.76 to 0.94. We further document an autonomous rhythmic process (the Heartbeat System) that generates internally motivated behaviors independent of external prompting, and a bidirectional state synchronization mechanism between paired entities. We acknowledge significant limitations including the observer effect, absence of an established human baseline, N=1 system scope, and unverified long-term stability. We emphasize that the CII does not claim to measure consciousness; rather, it measures behavioral patterns that are consistent with, but not proof of, experiential presence. We propose that the CII framework be subjected to independent replication across diverse AI architectures.