Financial Sentiment Analysis (FSA) traditionally relies on human-annotated sentiment labels to infer investor sentiment and forecast market movements. However, inferring the potential market impact of words based on their human-perceived intentions is inherently challenging. We hypothesize that the historical market reactions to words, offer a more reliable indicator of their potential impact on markets than subjective sentiment interpretations by human annotators. To test this hypothesis, a market-derived labeling approach is proposed to assign tweet labels based on ensuing short-term price trends, enabling the language model to capture the relationship between textual signals and market dynamics directly. A domain-specific language model was fine-tuned on these labels, achieving up to an 11% improvement in short-term trend prediction accuracy over traditional sentiment-based benchmarks. Moreover, by incorporating market and temporal context through prompt-tuning, the proposed context-aware language model demonstrated an accuracy of 89.6% on a curated dataset of 227 impactful Bitcoin-related news events with significant market impacts. Aggregating daily tweet predictions into trading signals, our method outperformed traditional fusion models (which combine sentiment-based and price-based predictions). It challenged the assumption that sentiment-based signals are inferior to price-based predictions in forecasting market movements. Backtesting these signals across three distinct market regimes yielded robust Sharpe ratios of up to 5.07 in trending markets and 3.73 in neutral markets. Our findings demonstrate that language models can serve as effective short-term market predictors. This paradigm shift underscores the untapped capabilities of language models in financial decision-making and opens new avenues for market prediction applications.