I've seen this effect in a lot of lyric video, particularly when the music is quite intense. Please see these videos for references:
There is a constant pulsating/flashing light effect
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The pulsating light is just the intensity of the light varying over time. There are various ways of doing that, you could keyframe it (if you had nothing better to do), you could use an expression like wiggle, or the "the wiggler" tool (if you're old school), or you could control it with the audio level of a layer that has audio.
If you're trying to drive the intensity of the light from the audio, then you need to first convert the audio levels to keyframes. Right-click the footage with the audio, and choose Animation>Keyframe Assistant>Convert Audio to Keyframes, or with the audio layer selected go to the Animation menu in the menu bar and choose *Keyframe Assistant>Convert Audio to Keyframes**. Then you can use those keyframes by either copying and pasting to your light's intensity property (and tweaking the values in the graph editor), or using an expression. This answer details how you do that.
You can do this in Apple's Motion using the Parameter > Audio behavior. Apply it to your audio track, then apply a Brightness filter to your footage and set the "Apply To" of the behavior to the filter's Brightness parameter. You'll need to adjust the parameters of the behavior to suite your audio and video.