Inline code suggestions from assistants such as GitHub Copilot appear and disappear quickly, shift position with scrolling, and range from single-line completions to multi-line overlays. For researchers studying how developers interact with these suggestions—especially with eye tracking—obtaining precise positional data, timing, and acceptance outcomes is highly challenging. Existing tools cannot track inline suggestions, since these overlays may disappear without ever being written into the source code. PosEyeDOM addresses this gap with a lightweight Chrome extension that operates in web-based VS Code environments such as GitHub Codespaces. It leverages the Document Object Model (DOM) to continuously log suggestion geometry, content, and timing, infer acceptance outcomes, and aggregate raw DOM changes into robust and labeled Areas of Interest (AOIs). It exports ready-to-use .ias files compatible with SR Research DataViewer and JSON dictionaries for custom pipelines, enabling scalable, suggestion-aware eye-tracking studies that were previously impractical. The extension further provides a live preview, remote export, and synchronization with external eye-tracking software, offering an all-in-one, plug-and-play workflow for empirical research on AI-assisted programming.