But there's something I don't understand.

If this noise is a "cue tone", then why is it occuring in the middle of
the "Local on the 8s", right after the voice-over announces "Our local
doppler radar"?

Aren't these forecasts seen at exactly 8, 18, 28, and so on, past the
hour - across the entire US?

For a more accurate description of the sound, turn your bicycle upside
down, spin the rear wheel good and fast, take a straw or twig, and let
it hit the spokes - interemittently.
t-t-t-t-t.......t-t-t-t-t-t...t-t-t--t-t- etc. Right as the doppler
radar shows.

-CC