We have very little information about Gershom or his brother Eliezer. Like many other children of famous fathers, they possibly shunned the limelight. Maybe they even turned away from Moses’ teachings.
Perhaps this explains a strange phenomenon in the Book of Judges (18:30) which refers to an idolater-priest called Jonathan the son of Gershom the son of Menasheh.
The Hebrew text of Judges does not actually spell the name Menasheh in the normal fashion. Between the mem and the shin there is a nun suspended above the line. Some say that the original word was mem-shin-heh, i.e. Moshe, and Jonathan was the son of Moshe’s son Gershom. What a come-down for Moses’ family!
The sages say the nun was inserted in order to disguise the name Moshe and so as not to embarrass the memory of the great leader (see Rashi), and it was a nun that was inserted to link Jonathan with Menasheh, the later king who was known for his wickedness.
Without blaming Moses for what became of his grandson or for that matter, blaming Gershom for his son Jonathan, we have to say that the price a leader often pays is that he has too little time for his children and grandchildren.
However, the whole Moshe-Menasheh theory is rendered problematical by the fact that the text in Judges actually speaks of Gershom and Jonathan being of the tribe of Dan, when Moses was from Levi.