Surely an ultra-rationalist like you would quickly realize that it is impossible to simultaneously ask what it means to be yeshivish, and label another person as being such.
Also, the Rambam, rationalist as he was, still believed in Divine intervention, which is a purely irrational conclusion. He also believed that the world was created, i.e. has a beginning, even though Aristotle himself could not support such a statement with any logical proof. One cannot be a believing Jew without accepting fundamental tenets which are not based in pure logic. But when you think about it, it is impossible for someone to live his life based on pure logic. For example, the fact that A caused B cannot prove that given another opportunity, A will in fact cause B in the future. Yet no one thinks twice about getting on a plane, or turning the ignition in a car. We live life based on assumptions, or experiential proof, i.e. we assume things to be true because they have shown themselves to be.
Enough of my rant against “rational” Judaism. Be whatever kind of Jew you want to be, as long as it is within the confines of Halachah.