We propose several localized sensor area coverage protocols, for arbitrary ratio of sensing and transmission radii. Sensors are assumed to be time synchronized, and active sensors are determined at the beginning of each round. The approach has a very small communication overhead since prior knowledge about neighbor existence is not required. Each node selects a random timeout and listens to messages sent by other nodes before the timeout expires. Sensor nodes whose sensing area is not fully covered (or fully covered but with a disconnected set of active sensors) when the deadline expires decide to remain active for the considered round, and transmit a message announcing their activity status. There are four variants in our approach, depending on whether or not negative and retreat messages are transmitted. Experimental results with ideal MAC layer show that, for a similar number of selected active sensors, our methods significantly reduce number of messages to decide activity compared to existing localized protocol, We also consider a MAC layer with collisions, and show that existing compared method, for dense networks, fails to cover the area reasonably. Our methods, however, still remain robust in terms of high area coverage with reasonable amount of active nodes, despite some message collisions.