"Sign off on" – I Get It!

Is anyone else annoyed?  “The board would have to sign off on any deal.”  – Wall Street Journal

Yes, "off on" has bugged me, off and on for years, as it did a Grammarphobia reader who asked for explanation.  But it's OK.  Now I get it, thanks to a writer smarter than I (am).

"... there is no contradiction.  ...  [adverb "off" like "pay off", preposition "on" meaning "concerning"]

There are many examples [just what I needed] ...  A speaker may go 'off on' a tangent, a ballplayer go 'out in' a blaze of glory, and a soggy person come 'in out' of the rain.  ...  The phrase 'sign off on' originated in the US in the first half of the 20th century, according to the Oxford English Dictionary."  – grammarphobia.com/blog/2012/09

No more irritation – that’s imperative (commanding myself).  That settled, I will relax soon by walking out in the sun.

Cousins connected in SLC sun at Ensign Peak, 14 September 2013