The use of ultra-high dose rate beams (UHDR) (> 40 Gy/s) for radiotherapy, despite its advantage of exhibiting the FLASH effect that improves the sparing of healthy tissues, faces challenges in dosimetry and beam monitoring since standard dosimeters like the ionization chamber experience saturation effects at such high dose rates. Silicon carbide (SiC) detectors have recently been demonstrated to be dose-rate independent with low-energy pulsed electron beams up to an instantaneous dose rate of 5.5 MGy/s, and has emerged as a reliable alternative technology for dosimetry in FLASH-RT. This study explored the suitability of using the SiC detector for measuring intra-pulse instantaneous dose rates, which are necessary for monitoring fluctuations within the pulse of UHDR pulsed electron beams. The experiments reported were conducted using UHDR electron beams accelerated at 9 MeV by an ElectronFlash linac and using varying different beam parameters, such as the beam current (i.e., different dose per pulse) and pulse width settings. The temporal single pulse shape signals were measured with a 10 µm thick, 4.5 mm2 area SiC detector for different configurations and compared with a well-characterized AC current transformer (ACCT) (which served as the standard monitoring system of the accelerator), and with a second ACCT placed at the same location as the SiC detector (i.e., after the applicator at the irradiation point). The results show a high level of agreement between the signals of the SiC detector and ACCT placed after the applicator at around the irradiation point. This underscores the potential of the SiC detector and the ACCT to be used for monitoring instantaneous dose rates within a pulse. Furthermore, since use of the SiC detector and ACCT are based on different physical principles, they can provide complementary beam information. A combination of the two has the potential to provide insight about a variety of variables of interest for UHDR beams. However, some discrepancies were observed when comparing the SiC signals with the ACCT installed in the LINAC, which increased linearly with decreasing dose per pulse. Further studies are required to better understand these observations.