Diagnosis
That's the HomePod Mini's 'I'm having a software tantrum' light. It's usually a corrupted software update or a glitch that happened during a restart.
How to Fix It
You need to force a restart. Unplug it from power, wait a full 10 seconds, then plug it back in. As soon as the white light appears, touch and hold the top of the HomePod. Keep holding until you hear three beeps and see the light turn red—then let go. It'll restart and should come back up with a pulsing white light while it sorts itself out.
If That Didn't Work
If the blinking persists, you'll have to factory reset it. Unplug it, plug it back in, wait 5 seconds, then press and hold your finger on the top. Keep holding even after the red light appears—after about 10 more seconds, Siri will say it's about to reset. Let go and wait for the setup tone.
Heads Up
The reset removes it from your Home and Apple ID. You'll have to set it up again like it's brand new, so make sure you know which Apple ID you used originally.