Incipient inter-turn short-circuit (ITSC) faults in permanent magnet synchronous machines (PMSMs) pose substantial diagnostic challenges, particularly under transient operating conditions common in electric vehicle (EV) applications. Traditional frequency-domain techniques, such as the Fast Fourier Transform (FFT), exhibit poor time-frequency resolution, making them ineffective for capturing non-stationary fault signatures. This study employs FEM-based numerical simulations combined with Continuous Wavelet Transform (CWT) analysis to accurately detect and localize ITSC fault characteristics under dynamic load conditions. While magnetic saturation is known to influence machine behavior, its quantitative impact on electrical fault signal amplitudes has not been explicitly addressed in previous diagnostic approaches. To fill this gap, a high-fidelity FEM simulation framework was developed, encompassing the full operational envelope of PMSMs. The results demonstrate that magnetic saturation leads to a notable attenuation-approximately 20-30% - of fault-induced current components, significantly complicating onboard detection. To the best of the authors' knowledge, such an integrated, EV-specific onboard diagnostic approach for incipient ITSC faults has not yet been reported in the literature. Although onboard thermal management systems exist, incipient ITSC faults may rapidly escalate into severe winding damage within 10 to 60 minutes under continuous load. This highlights the critical need for early detection methods robust to transient dynamics and magnetic nonlinearities.