In human conversations, short backchannel utterances such as "yeah" and "oh" play a crucial role in facilitating smooth and engaging dialogue. These backchannels signal attentiveness and understanding without interrupting the speaker, making their accurate prediction essential for creating more natural conversational agents. This paper proposes a novel method for real-time, continuous backchannel prediction using a fine-tuned Voice Activity Projection (VAP) model. While existing approaches have relied on turn-based or artificially balanced datasets, our approach predicts both the timing and type of backchannels in a continuous and frame-wise manner on unbalanced, real-world datasets. We first pre-train the VAP model on a general dialogue corpus to capture conversational dynamics and then fine-tune it on a specialized dataset focused on backchannel behavior. Experimental results demonstrate that our model outperforms baseline methods in both timing and type prediction tasks, achieving robust performance in real-time environments. This research offers a promising step toward more responsive and human-like dialogue systems, with implications for interactive spoken dialogue applications such as virtual assistants and robots.