The ultra-wide Terahertz (THz) band with jointly high-speed transmission and precise sensing has come into vision to realize integrated sensing and communication (ISAC) for emerging immersive applications. However, THz networks face a coverage bottleneck. Narrow beams are exploited to compensate for the limited signal power and path loss. But they bring in beam misalignment that degrades link connectivity and affects the THz network coverage, characterized by coverage probability. ISAC-THz networks can benefit from the sensing-aided beam alignment to improve the coverage probability. But there exists a trade-off between sensing assistance and its cost, that requires efficient resource allocation. This paper provides time-frequency resource allocation for sensing signal mapping schemes that maximize the coverage probability of the ISAC-THz networks with reduced sensing costs. Results show the effectiveness of the scheme in reducing the sensing cost with near-ideal coverage. We reveal design insights into the sensing signal insertion and preferable THz transmission band selection that achieves the desired coverage with the least sensing overhead. Wider coverage requires more sensing resources, which are more allocated to bandwidth for accurate long-range sensing. The high angular resolution of narrow beams helps reduce the sensing cost, sparing resources in the time domain for velocity estimation.