Stance detection in social media is challenging, as interpreting a text often requires understanding the author's perspective. We re-frame political stance detection as an author-informed text understanding task, where it is desired to infer both the author's political leaning and their stance towards the target from the text. We first show that human annotators struggle to infer authors' political leanings and stances from individual tweets, and that pretrained large language models (LLMs) perform below human level in this setting. We then demonstrate that author context improves stance detection for both humans and LLMs, with particularly pronounced benefits for tweets perceived as sarcastic. Through extensive experiments, we further show that LLMs can be effectively fine-tuned to predict authors' political affiliations, and that author-informed fine-tuning yields better stance detection performance than standard fine-tuning. This approach not only surpasses human performance but also improves generalization across datasets. To support further research on author-informed political stance detection, we release a large dataset of stance-labeled tweets enriched with author-context information.