Where is the term "Separation of Church and State" in any Amendment to the Constitution.
You show a profound misunderstanding of both history and Constitutional law. In any law, and the constitution is just a species of law albeit more fundamental, words are not always self defining. In fact, much of the language of the Constitution is purposefully vague and ambiguous. The reason is simple, language is not precise enough to think of all the particular applications of principles, so you state the principles and leave it to those who decide particular cases to put the flesh on the bone so to speak.
Case in point, there is nothing in the Constitution that specifically says that Churches cannot be taxed. You can read it, there's nothing in there. However, it has long been a principle that Churches will not be taxed because that may inhibit the "free exercise" of a religion.
Another case in point, there is nothing in the Constitution that defines "commerce", yet Congress has the power to regulate interstate commerce. How could Congress possibly regulate something that is not defined? Simple, they enact regulations and the courts decide based on common definitions, tradition and precedent if what Congress is regulating is Commerce for constitutional purposes. That's how things work in our system.
To say that the phrase "separation of church and state" is not in the constitution, which of course that exact phrase is not, and then try to bootstrap that to mean that the separation of church and state was not intended is to ignore history, precedent and common sense.
BTW, as you probably know, Jefferson seems to be one of the originators of the phrase "separation of church and state", and as one of the principle founders, I would think his opinion on the subject should count heavily in interpreting what the language of the amendment was intended to mean.