Should an Ephraimite, a Jew, or any male person wear a Yarmulke / Kippah (skullcap) during prayer or Torah study?

Here is an interesting American Reform-based view: Men's Head Covering in Synagogue: Reform Judaism's Views. Three paragraphs from the article:

"From all of this, Lauterbach concluded that the custom of praying with covered head "is merely a matter of social propriety and decorum"' since in our own culture it is considered "good manners" to remove the hat as a sign of respect, there can be no objection to praying bareheaded. He writes: "Although in the last century the question of 'hat on or hat off' was the subject of heated disputes…we should know better now and be more tolerant and more liberal towards one another. We should realize that this matter is but a detail of custom and should not be made the issue between Orthodox and Reform. It is a detail that is not worth fighting about. It should not separate Jew from Jew.

One may quibble over Lauterbach's interpretation of a number of his sources. Some of them do not say precisely what he tells us that they say, and this tends to weaken his argument somewhat. His central point is certainly correct: Jewish law makes no absolute requirement that one cover the head to pray, to study Torah, or to participate in other religious acts. On the other hand, his conclusion -- that covering the head "is merely a custom, a minhag"; "merely a matter of social propriety" -- hardly reflects what is at stake in this issue, for surely he was aware that there is no such thing as "mere" custom in Judaism.

Much of Jewish ritual practice is based upon custom rather than upon Toraitic commandment or rabbinic decree, yet the tradition does not regard it as unimportant or irrelevant for that. As the old Ashkenazic saying puts it, "the custom of our ancestors is Torah." Jews have always related to their customs with intensity and seriousness. Fierce debates in Jewish religious life are as likely to take place over matters of "mere" custom as they are over issues of Torah law and theological doctrine."

The bold was mine. The ideal of Rabbinic "custom becoming TORAH" definitely appear prevalent even in Yeshua's time. In Mark 7:6-7, he quotes Isaiah 29:13:

“Inasmuch as these people draw near with their mouths And honor Me with their lips, But have removed their hearts far from Me, And their fear toward Me is taught by the commandment of men,"

So the question for Ephraim is this: If it is not commanded to wear a headcovering in the Torah, should you still listen to a command issued via man? You know... we can all come up with flowery explainations as to why we'll just keep the command anyway, but what does the Torah say about adding commandments to the Torah?

Deuteronomy 4:2: "You shall not add unto the word which I command you, neither shall you diminish from it, that you may keep the commandments of יהוה your Elohim which I command you."

The House of Ephraim not accepting/embracing the tradition of Judah’s elders is one of the primary reasons they won’t allow Ephraim to return to the Land of Israel in mass (as in the Bnei Menashe experience, Judah wants those returning to convert formally to Judaism). I for one will remain in exile if the condition is I must embrace their man-made commandments or live in Israel as many Messianics do and succumb to Rabbinic pressure to follow their halakha. Many just put their kippah or hat on so the Orthodox won’t hassle them to death. It isn’t out of respect in many cases... it is protectionism or self-preservation.