This might seem a little unconventional, but rather than having the Tamaduino's hardware hooked up to a steady power supply, I want to introduce the concept of stamina. I'm thinking of achieving that by using a 1F super-capacitor as primary power source. The capacitor will deplete much more quickly than a battery, but slow enough to allow the Tamaduino to do stuff.
Depending on the amount of charge stored in the capacitor, the Tamaduino's interactive abilities would change. When the charge drops below a certain level, the Tamaduino will have to rest while the Energy Brain activates a boost circuit and recharges the super-capacitor from a Li-Ion battery. If the charge in the Li-Ion battery drops below a certain level, the Tamaduino will start making an effort to motivate forces in the environment to move the Tamaduino to a location where its solar panel can recharge the Li-Ion battery. Simultaneously it would start changing its overall behavior to conserve as much energy as possible until it has eaten a sufficient amount of photons.
In some way I'm trying to mimic a biological energy metabolism. Humans ingest food and store the energy in different mediums. Some of them are accessible super quickly, like ATP, some of them require metabolizing, but are fast acting, like sugar, and some mediums, like fat, are very energy dense but take much more time and effort to be converted into biologically available energy.
In the Tamaduino's energy metabolism, sunlight would be the food; the Li-Ion battery would be the fat; the super-capacitor would be the glucose; and the distributed electrolyte- and ceramic capacitors would be like ATP. The comparison might be a little off, but I hope my biology metaphors make sense.