Ishmael must have been a man of sufficient faith and humility to respond to such a bold invitation. Unfortunately, we do not learn much more about Ishmael from the record.
How Do We Know That Ishmael Was from the Tribe of Ephraim
In The Articles of Faith, James E. Talmage cites the prophet Joseph as teaching the doctrine that Ishmael was from Ephraim:
"Ishmael an Ephraimite – 'The Prophet Joseph Smith informed us that the record of Lehi was contained on the one hundred sixteen pages that were first translated and subsequently stolen, and of which an abridgment is given us in the First Book of Nephi, which is the record of Nephi individually, he himself being of the lineage of Manasseh; but that Ishmael was of the lineage of Ephraim, and that his sons married into Lehi's family, and Lehi's sons married Ishmael's daughters, thus fulfilling the words of Jacob upon Ephraim and Manasseh in the 48th chapter of Genesis [verse 16] which says: 'And let my name be named on them, and the name of my fathers Abraham and Isaac; and let them grow into a multitude in the midst of the earth.' Thus these descendants of Manasseh and Ephraim grew together upon this American continent, with a sprinkling from the house of Judah, from Mulek descended, who left Jerusalem eleven years after Lehi, and founded the colony afterwards known as Zarahemla found by Mosiah -- thus making a combination, an intermixture of Ephraim and Manasseh with the remnants of Judah, and for aught we know, the remnants of some other tribes that might have accompanied Mulek. And such have grown up upon the American continent.' -- From "Discourse by Apostle Erastus Snow," at Logan, Utah, May 6, 1882, see Journal of Discourses, vol. 23, pp. 184, 185." (James E. Talmage, A Study of the Articles of Faith, p.504-5)