This paper presents a model-free Best Efficiency Point (BEP) tracking method for centrifugal pumps without head measurement or manufacturer-provided characteristic curves. The proposed approach combines a discrete finite-difference extremum-seeking control (ESC) scheme with an efficiency approximation proxy derived from measurable variables—namely, flow rate and electrical power. Under constant head conditions, the proxy function is analytically shown to be proportional to the true pump efficiency, enabling real-time BEP localization using only motor feedback signals. The ESC algorithm employs a sign-based gradient rule with adaptive step-size reduction to achieve rapid and stable convergence without mathematical models. A Python-based simulation using a Schneider SUB 15-0.5cv pump demonstrates that the method can track the BEP with negligible steady-state error (less than 0.1% efficiency deviation). The proposed framework offers a cost-effective solution for efficient optimization for mobile pumping applications in large water resources where installing head sensors is impractical.