Neuromorphic computing, inspired by the biological mechanisms of neural signal transmission, has emerged as a promising technology for efficient and parallel data processing with minimal power consumption. In this study, we developed floating-gate organic thin-film transistors (OTFTs) with self-assembled monolayer (SAM)-based tunneling layers to mimic the characteristics of artificial synapses. The tunneling layers were formed using mixed phosphonic acid SAMs with varying ratios of octadecylphosphonic acid (ODPA) and 12-pentafluorophenoxydodecylphosphonic acid (PFPA). The influence of these ratios on the memory and neuromorphic characteristics of the devices was systematically evaluated. Our results revealed that the ODPA ratio significantly impacts the hysteresis window, with higher ODPA content yielding improved memory characteristics. Conversely, the PFPA : ODPA ratio of 2:1 exhibited the lowest non-linearity (NL = 0.48), demonstrating the potential for highly accurate weight updates in neuromorphic devices. Additionally, pulse width modulation studies showed that a pulse width of 100 ms optimized the linearity and stability of long-term potentiation (LTP) and depression (LTD) characteristics. The combination of sol-gel processed AlOx as a floating-gate layer and tailored SAM-based tunneling layers allowed for precise control of device performance. These findings highlight the importance of molecular engineering in designing SAM layers to balance memory retention and neuromorphic functionality. This study provides a pathway for advancing organic floating-gate transistors as a core component in next-generation neuromorphic computing systems.