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The ICARUS liquid argon time projection chamber (LArTPC), operating as part of the Fermilab Short-Baseline Neutrino (SBN) program, detects neutrinos by capturing ionization electrons and scintillation photons produced in neutrino—argon interactions. The scintillation photons are collected by photomultiplier tubes (PMTs), which convert light into electrical signals used for event reconstruction and triggering. In 2023, a new hardware component known as the adder board was introduced to improve the light-trigger efficiency for low-energy neutrino events (<300 MeV). This board sums, reshapes, and outputs the analog signals from 15 neighboring PMT channels to help identify potential neutrino interactions. This work presents the first simulation of the adder-board electronics response and its validation against ICARUS data. The simulated waveforms reproduce detector data with 93.2% agreement in signal amplitude, demonstrating accurate modeling of the adder-board response. The validated model will be integrated into the ICARUS trigger-simulation framework, enabling more accurate detector simulations and improved detection of low-energy neutrino events.