Underwater visible light communication (UVLC) is a high capacity wireless connectivity solution with low latency, particularly appealing for real-time underwater video and image transmission. While attenuation and geometrical losses determine the average light intensity, underwater optical turbulence introduces fluctuations on the average received intensity, also known as fading. Due to relative movements of source and/or detector in harsh underwater environment, pointing errors further cause additional fading. In this paper, we consider a vertical underwater link modeled as a multi-layer channel where the fading coefficients associated with each layer are modeled as independent but not identically distributed Gamma-Gamma random variables. We model the displacements along the horizontal and elevation axes as independent and identically distributed Gaussian variables. Under these assumptions, we derive a closed-form expression for bit error rate (BER) expression. Based on asymptotical BER analysis, we determine the diversity order as a function of system and channel parameters. We further present Monte-Carlo simulation results to confirm the derived expressions.