How does Tsongkhapa understand the "insight" into emptiness?

Tsongkhapa and the Gelug school in general place great emphasis on the analysis of the emptiness of each thing. However, after this analysis, they also insist on having an "insight" into this object. It is, so to speak, like seeing "floaters" in my eyes and my doctor telling me that it is an ocular problem, not actual flies. I still have the experience of seeing flies, but I know that the object of this perception is an ocular condition. If I undergo surgery, this object is also confirmed subjectively, phenomenologically, and my experience aligns with the object. Something similar happens with the method Tsongkhapa proposes. What I want to know is: what kind of *act* does Tsongkhapa understand this to be? Is it a non-conceptual *perception*? Is it an *intuition*?