Mechanisms for orienting toward and locating an odor source are sought in both biology and engineering. Chemical ecology studies have demonstrated that adult female sea lamprey show rheotaxis in response to a male pheromone with dichotomous outcomes: sexually mature females locate the source of the pheromone whereas immature females swim by the source and continue moving upstream. Here we introduce a simple switching mechanism modeled after odor-conditioned rheotaxis for the sea lamprey as they search for the source of a pheromone in a one-dimensional riverine environment. In this strategy, the females move upstream only if they detect that the pheromone concentration is higher than a threshold value and drifts down (by turning off control action to save energy) otherwise. In addition, we propose various uncertainty models such as measurement noise, actuator disturbance, and a probabilistic model of a concentration field in turbulent flow. Based on the proposed model with uncertainties, a convergence analysis showed that with this simplistic switching mechanism, the lamprey converges to the source location on average in spite of all such uncertainties. Furthermore, a slightly modified model and its extensive simulation results explain the behaviors of immature female lamprey near the source location.