Federated Learning (FL) systems orchestrate the cooperative training of a shared machine learning (ML) model across connected devices. Recently, decentralized FL architectures driven by consensus have been proposed to enable the devices to share and aggregate the ML parameters via direct sidelink communications. The approach has the advantage of promoting the federation among the agents even in the absence of a server, but may require an intensive use of communication resources compared to vanilla FL methods. This paper proposes a communication-efficient design of consensus-driven FL optimized for training of deep neural networks (DNNs). Devices independently select fragments of the DNN to be shared with neighbors on each training round. Selection is based on a local optimizer that trades model quality improvement with sidelink communication resource savings. The proposed technique is validated on a vehicular cooperative sensing use case characterized by challenging real-world datasets and complex DNNs typically employed in autonomous driving with up to 40 trainable layers. The impact of layer selection is analyzed under different distributed coordination configurations. The results show that it is better to prioritize the DNN layers possessing few parameters, while the selection policy should optimally balance gradient sorting and randomization. Latency, accuracy and communication tradeoffs are analyzed in detail targeting sustainable federation policies.