As you mentioned, this thing is just a timer to save some battery capacity. Eventually it can be a dimmer that reduces intensity over time to make it a 'kids sleep lamp'.
After a good clean this might still work. It is a very simple schematic. Rinse it with water and a eventually a mild detergent. You might want to use a mild brush like a toothbrush. Dry it well before powering up. Make sure there is no moisture under the chip. Measure all the traces to check them.
J3Y is probably a S8050 transistor. See pic borrowed from the internet