To cover or spot with spots; to mark with spots or stains (very rare or obsolete).
From 'be-' (to cover with) plus 'spout' (a spot or stain), though the etymology is uncertain. This appears to be an extremely rare or possibly nonce-word formation, possibly confused with 'bespatter' or similar be- verbs.
Words like 'bespout' are linguistic fossils—they appear once or twice in old texts and then vanish, teaching us that not every word formation stuck, and that understanding why some morphological patterns failed helps us see what sounds natural to language.
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