Vision-language models (VLMs) achieve strong performance on multimodal benchmarks, but may still lack robust control over basic visual operations. We study \textit{line tracing}, where a model must follow a selected visual path through successive local continuations. To isolate this ability, we design controlled tracing tasks that introduce nearby competitors while reducing semantic and topological ambiguity such as crossings and overlaps. Across these tasks, even state-of-the-art VLMs frequently lose the target path and switch to nearby alternatives, especially when those alternatives look locally similar to the target. Behavioral interventions and internal analyses indicate that these failures arise from local competition: nearby similar distractors pull the model away from the true continuation. Standard remedies do not remove this bottleneck: model-size scaling provides only limited gains, reasoning partially compensates through costly substitute strategies, and explicit tracing instructions fail to recover stable path following. Finally, tests on tangled-cable scenes and metro maps with richer visual complexity show that the same path-switching failure persists beyond our controlled settings.