The cross-cache attack is a fundamental component of modern Linux kernel exploits, spanning real-world attacks and recent research. Despite its importance, it is often regarded as unreliable due to its complex setup, and existing studies lack in-depth analysis of its mechanics. In this paper, we address this gap by: (1) reviewing public strategies and their limitations, (2) proposing two optimized strategies effective in varied conditions, and (3) introducing CROSS-X, an automated system that identifies suitable target objects for cross-cache attacks. We evaluated our strategies on a synthetic vulnerability and nine real-world CVEs, achieving over 99% and 85% success rates under idle and busy workloads, respectively. They also outperformed existing methods in 6 of 8 CVEs under idle workloads and 5 of 8 under busy workloads. For object identification, we define three key properties: (1) spray capability, (2) minimal interference, and (3) useful primitives. Based on these, CROSS-X identified seven versatile target objects and their relationship with interfering allocations. We believe our work will enhance public understanding of cross-cache attacks and contribute to improving Linux kernel security.