Is "Number Second" correct as in "he became number second"?

I don't think so. I've search for usage of the phrase "number second" but couldn't fine any credible source opting to use it. I believe that "second" would fit better:"When we added Sign in with Google in May, it took off becoming number one and email becoming the second." But since English isn't my native language, I'm not so certain about it.

When we enumerate items it is conventional to keep the same construction throughout the list: number 1, number 2, ... ; the first, the second, the third ... .

Mixing the forms of construction is at least bad style, and perhaps ungrammatical. Furthermore, number first, number second ... is not conventionally used in listing; I have never encountered it. Adjectives like First and Second are two of many adjectives that are not enumerable in this way. Number green, number red ... ? Almost meaningless.