"Incite" - This word means to encourage or stir up, which can be related to the process of gaining insight, but it's not a direct synonym.
"Incite" can be used in a phrase like "The new data incited a deeper understanding of the problem." This doesn't directly mean "insight," but it does hint at the process of gaining knowledge.
While these words don't share the exact meaning, they can be used in ways that capture a similar concept. However, it's important to remember that they are not true homonyms and have distinct meanings.