Why do my new LED Christmas lights glow faintly after the timer shuts them off?

That faint glow is a real LED quirk, and it drives plenty of people nuts. An LED needs almost no current to light up, so any little bit of stray voltage in the strand makes them ghost at you. Incandescents need a real load before they'll glow at all, which is why your old strings snapped dark the instant the timer cut power.

Had the same ghosting problem on my porch strands last winter and it nearly drove me up the wall. Turned out my timer was one of the digital kind, and those let a trickle of current through even when they're off. What fixed it for me was plugging a single old-school incandescent nightlight into the same outlet on the timer. It soaked up that stray bit of voltage and the LEDs went fully dark. Might be worth checking if your timer is the digital type or the little motorized dial kind, since the dial ones actually break the circuit all the way.

Same thing happened on my eaves two years ago and it wasn't the timer at all. I had the dead strand zip tied right next to a live extension cord running the length of the gutter, and the powered cord was enough to make the neighboring LEDs glow faintly. Moved the extension cord to the other side of the fascia and the ghosting stopped completely. Worth checking what's running beside your strands before you blame the timer.