This study investigates multimodal turn-taking prediction within human-agent interactions (HAI), particularly focusing on cooperative gaming environments. It comprises both model development and subsequent user study, aiming to refine our understanding and improve conversational dynamics in spoken dialogue systems (SDSs). For the modeling phase, we introduce a novel transformer-based deep learning (DL) model that simultaneously integrates multiple modalities - text, vision, audio, and contextual in-game data to predict turn-taking events in real-time. Our model employs a Crossmodal Transformer architecture to effectively fuse information from these diverse modalities, enabling more comprehensive turn-taking predictions. The model demonstrates superior performance compared to baseline models, achieving 87.3% accuracy and 83.0% macro F1 score. A human user study was then conducted to empirically evaluate the turn-taking DL model in an interactive scenario with a virtual avatar while playing the game "Dont Starve Together", comparing a control condition without turn-taking prediction (n=20) to an experimental condition with our model deployed (n=40). Both conditions included a mix of English and Korean speakers, since turn-taking cues are known to vary by culture. We then analyzed the interaction quality, examining aspects such as utterance counts, interruption frequency, and participant perceptions of the avatar. Results from the user study suggest that our multimodal turn-taking model not only enhances the fluidity and naturalness of human-agent conversations, but also maintains a balanced conversational dynamic without significantly altering dialogue frequency. The study provides in-depth insights into the influence of turn-taking abilities on user perceptions and interaction quality, underscoring the potential for more contextually adaptive and responsive conversational agents.