I know for a fact that there is another character which constitutes the same symbol but flipped. Thanks.

Adobe Wood Type Ornaments  Suggested by pilaster 

This the one?

That looks close. Thanks. However, the only character that constitutes that dingbat is one that has both ends. I’m searching for two separate characters, each bearing a single end of the character. Do you have any suggestions?

I can't think of a font with that as a glyph. (Others may offer one yet)
Cant you just flip or rotate the sample? Use that as a placed graphic element?
If I'm reading your post correctly, what you want is this.