Channel equalization is fundamental for mitigating distortions such as frequency-selective fading and inter-symbol interference. Unlike standard supervised learning approaches that require costly retraining or fine-tuning for each new task, in-context learning (ICL) adapts to new channels at inference time with only a few examples. However, existing ICL-based equalizers are primarily developed for and evaluated on static channels within the context window. Indeed, to our knowledge, prior principled analyses and theoretical studies of ICL focus exclusively on the stationary setting, where the function remains fixed within the context. In this paper, we investigate the ability of ICL to address non-stationary problems through the lens of time-varying channel equalization. We employ a principled framework for designing efficient attention mechanisms with improved adaptivity in non-stationary tasks, leveraging algorithms from adaptive signal processing to guide better designs. For example, new attention variants can be derived from the Least Mean Square (LMS) adaptive algorithm, a Least Root Mean Square (LRMS) formulation for enhanced robustness, or multi-step gradient updates for improved long-term tracking. Experimental results demonstrate that ICL holds strong promise for non-stationary MIMO equalization, and that attention mechanisms inspired by classical adaptive algorithms can substantially enhance adaptability and performance in dynamic environments. Our findings may provide critical insights for developing next-generation wireless foundation models with stronger adaptability and robustness.