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Figured there was enough space in the PG unicorn base to add something else besides the arduino.
2x rechargable 18650 cells from an old laptop battery in parallel, amazingly after 8 years still hold charge, About 1600mAh each to be exact.
Connected to a charge circuit with overcharge and short circuit protection built in, which in turn is connected to a boost circuit (since the 3.7v-4.2v supplied by the battery needs to be a clean 5v for the arduino)
Using a usb breakout board to power it since I can position that wherever I like in the base.
Battery indicator circuit attached to the battery wiring, press the button and the leds tell you the charge state based on the output voltage.