If the app doesn't register clicks in a specific game, check if the app requires "Accessibility Services" to be enabled in your Android settings on the Chromebook.

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The most reliable way to get an auto clicker on a restricted Chromebook is to use the native accessibility tool. Since it is a part of ChromeOS, it cannot be "blocked" in the traditional sense.

If your Chromebook has enabled (found under Settings > Developers), you can install professional-grade auto clickers that bypass ChromeOS's app restrictions entirely. The Tool: XClicker is a popular open-source choice.