Post-translational modification of tubulin provides differential functions to microtubule networks. Here, we address the role of tubulin acetylation on the penetrative capacity of cells undergoing radial intercalation, which is the process by which cells move apically, insert between outer cells, and join an epithelium. There are opposing forces that regulate intercalation, namely, the restrictive forces of the epithelial barrier versus the penetrative forces of the intercalating cell. Positively and negatively modulating tubulin acetylation in intercalating cells alters the developmental timing such that cells with more acetylation penetrate faster. We find that intercalating cells preferentially penetrate higher-order vertices rather than the more prevalent tricellular vertices. Differential timing in the ability of cells to penetrate different vertices reveals that lower-order vertices represent more restrictive sites of insertion. We shift the accessibility of intercalating cells toward more restrictive junctions by increasing tubulin acetylation, and we provide a geometric-based mathematical model that describes our results.