The custom of Rosh Chodesh Elul apparently had no special tradition in the TaNaKh or in early Rabbinic writings. Rosh Chodesh Elul customs became established well into the first millennium (e.g. Rashi, Rabbi Judah Loew of Prague and others) that designated Elul as the time to prepare for the High Holy Days (not to say this thinking didn't exist previously).
"Because these days are filled with so much meaning and potency, they require a special measure of readiness. All the month of Elul, before eating and sleeping, a person should search his soul and his deeds, that he may make confession.”
(Rabbi Judah Loew, 1525-1609)
"Most of us are used to hearing the shofar during the months of Elul and Tishrei only, when in fact, in the past; the use of the shofar was far more commonplace."
Found this following link to be most interesting ...
http://www.shofarcall.com/teaching---how---when--where.html ... This link is more representative of the Jewish Roots of Christianity (e.g. Dr. Michael Brown, Pastor Larry Huch and others); however it shouldn't be offensive to Messianic Judaism. If any one believes any of the information in this link isn't accurate please let us know ... Thanks