In this study, the bipartite time-varying output formation tracking problem for heterogeneous multi-agent systems (MASs) with multiple leaders and switching communication networks is considered. Note that the switching communication networks may be connected or disconnected. To address this problem, a novel reduced-dimensional observer-based fully distributed asynchronous dynamic edge-event-triggered output feedback control protocol is developed, and the Zeno behavior is ruled out. The theoretical analysis gives the admissible switching frequency and switching width under the proposed control protocol. Different from the existing works, the control protocol reduces the dimension of information to be transmitted between neighboring agents. Moreover, since an additional positive internal dynamic variable is introduced into the triggering functions, the control protocol can guarantee a larger inter-event time interval compared with previous results. Finally, a simulation example is given to verify the effectiveness and performance of the theoretical result.