Green’s Dictionary of Slang

an indiscreet talker.

1850		E.V. Kenealy Goethe: a New Pantomime in Poetical Works 2 (1878) 335: Reptile, Squabbler, Puppy, Sneak, / Blobberlip, Wasp, Crackbrain, Buffer.
[1896		G.F. Northall Warwickshire Word-Book 31: Blobmouthed. Talkative].
1949		PADS XI 3: Blobber-mouth [...] A talkative person; one who will not keep a secret.
1954		Harder Collection [DARE].
1958		R. Chase Amer. Folk Tales 82: I done told you to keep that blobber mouth shut.
1969		in DARE.