This is normal behavior of the mouse.
The green battery light of your G7 mouse will come on for a few seconds to indicate the battery condition and then will go out. This happens when you power on your mouse or when the mouse is about to go idle.
When the mouse is in motion, the green battery light will go out and the battery levels are replaced with orange lights to indicate the current dpi setting.

Important Notice: The Firmware Update Tool is no longer supported or maintained by Logitech. We highly recommend using Logi Options+ for your supported Logitech devices. We are here to assist you during this transition.
Important Notice: The Logitech Preference Manager is no longer supported or maintained by Logitech. We highly recommend using Logi Options+ for your supported Logitech devices. We are here to assist you during this transition.
Important Notice: The Logitech Control Center is no longer supported or maintained by Logitech. We highly recommend using Logi Options+ for your supported Logitech devices. We are here to assist you during this transition.
Important Notice: The Logitech Connection Utility is no longer supported or maintained by Logitech. We highly recommend using Logi Options+ for your supported Logitech devices. We are here to assist you during this transition.
Important Notice: The Unifying Software is no longer supported or maintained by Logitech. We highly recommend using Logi Options+ for your supported Logitech devices. We are here to assist you during this transition.
Important Notice: The SetPoint software is no longer supported or maintained by Logitech. We highly recommend using Logi Options+ for your supported Logitech devices. We are here to assist you during this transition.
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