This study explores adaptive output feedback leader-following in networks of linear systems utilizing switching logic. A local state observer is employed to estimate the true state of each agent within the network. The proposed protocol is based on the estimated states obtained from neighboring agents and employs a switching logic to tune its adaptive gain by utilizing only local neighboring information. The proposed leader-following protocol is fully distributed because it has a distributed adaptive gain and relies on only local information from its neighbors. Consequently, compared to conventional adaptive protocols, the proposed design method provides the advantages of a very simple adaptive law and dynamics with a low dimension.