Quantum random number generators (QRNGs) based on homodyne measurements of vacuum fluctuations are in high-demand as fast and secure sources of randomness for vital applications such as cryptographic protocols. Despite the high volume of research, most implementations rely on a balanced homodyne detection (BHD) scheme with a continuous-wave local oscillator. Typically, these operate under the assumption that electronic noise levels remain constant throughout large spans
of time. In this work, we propose and analyse a suitable setup for a QRNG based on BHD using a pulsed local oscillator. Contrarily to previous schemes, this implementation introduces the possibility of real-time electronic noise monitoring, which can help increase robustness against attacks. The experimental setup is characterized to assess the conditions where quantum fluctuations are dominant. Finally, we compare it with the more traditional continuous-wave implementation and highlight the advantages of each implementation.