Auto-turn-on back light for kids toy shelf in the morning

Goal: light behind the kids' toy shelf comes on automatically each morning. Need to figure out: - Will the existing in-wall smart plug work, or does the digital on/off switch on the light fixture break that approach? (At least one of the lights has a digital switch, not a mechanical one.) - If smart plug won't work → research alternatives (smart bulb, Lutron Caseta-style switch replacement, Hue dimmer, etc.) - Pick a solution and schedule the morning-on automation.