This sentiment seems to be strongly related to the 'paradox of hedonism'. In short: Pursuing happiness itself may not lead to happiness. Pursuit of something other (greater?) than happiness may in fact result in higher levels of happiness.

"Unfortunately for the hedonist, constant pleasure-seeking may not yield the most actual pleasure or happiness in the long run—or even in the short run, when consciously pursuing pleasure interferes with experiencing it."

https://en.wikipedia.org/wiki/Paradox_of_hedonism

John Stuart Mill: "Ask yourself whether you are happy, and you cease to be so."