Why is "dingbat" used to refer to characters like "☺"?

A dingbat is "an ornamental piece of type for borders, separators, decorations, etc." as well as a silly person. The fonts are called dingbat fonts because they contain such characters.

The word's etymology leads me to believe that it is a generic word, akin to widget, doohickey, and thingamajig.

Dingbat is a typographical device other than a letter or numeral (such as an asterisk), used to signal divisions in text or to replace letters in a euphemistically presented vulgar word.

ORIGIN mid 19th cent. (in early use applied to various vaguely specified objects): origin uncertain; perhaps based on obsolete ding [to beat, deal heavy blows.]

I also think that the correlation with its other sense (a stupid or eccentric person) is rather apparent.