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In status update systems, multiple features carried by the status updating process require pursuit of objectives beyond timeliness measured by the age of information of updates. We consider such a problem where the transmitter sends status update messages through a noiseless binary energy harvesting channel that is equivalent to a timing channel. The transmitter aims to amplify or mask the energy state information that is carried in the updating process. The receiver extracts encoded information, infers the energy state sequence while maintaining timeliness of status updates. Consequently, the timings of the updates must be designed to control the message rate, the energy state uncertainty, and the age of information. We investigate this three-way trade-off between the achievable rate, the reduction in energy arrival state uncertainty, and the age of information, for zero and infinite battery cases.