Gabble indicates a speaker is overwhelmed by emotions which makes their speech rushed and unclear. When she heard the news, she started to gabble with joy, barely coherent.
Pro Tip 2/3
Informality
Gabble is used in casual situations and would not be appropriate in formal writing or speech. At the family reunion, everyone was gabbling excitedly.
Pro Tip 3/3
Negative Nuance
Using 'gabble' can imply the speaker thinks the fast talk is annoying or hard to understand. Can you stop gabbling? I can't follow what you're saying.