Chain-of-thought (CoT) monitoring is increasingly treated as an important safety layer for frontier reasoning models. Most monitorability evaluations study explicit-influence settings: setups where the prompt directly incentivizes the model to hide something, e.g., by instructing it to perform a hidden side-task. A complementary axis for CoT-monitor evaluations is implicit-influence settings, where the prompt contains no instruction to hide, but the model's behavior is still shaped by features of the task or context, e.g. an irrelevant detail about a candidate that biases a hiring rating. We introduce the first benchmark that directly compares CoT monitorability under the two regimes. We test how model behavior changes in the presence of a nudge to choose a particular option. The nudge is delivered either as a casual aside (implicit), or as a direct instruction to act on the nudge and to conceal having done so (explicit). The benchmark spans four task formats (binary choice, numeric rating, multiple-choice QA, open-ended coding) and seven frontier extended-thinking models. Under explicit influence, a CoT monitor detects 60-94% of behavior shifts: even models instructed to conceal it leak the instruction into their CoT. Under implicit influence, the same factors still shift behavior, but detection falls by 41-46 percentage points in two of our four settings. Realistic system-prompt additions (of the kind a developer might deploy to reduce off-topic bias) lower implicit detection further, to as low as 5%, while preserving the behavioral influence itself. These results suggest that monitorability estimates obtained in explicit-influence settings may over-estimate monitorability, and that monitorability can be further decreased by well-intentioned deployment choices. Our benchmark and code are available at https://github.com/agatha-duzan/implicit-vs-explicit-influence

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