I’m sorry, but protein is essential for life, so it is “ketogenic” by definition. It does stimulate some insulin production, but at less than half the rate at which carbohydrate does. Fat barely stimulates insulin production at all, which is why it is the macronutrient of choice for people who want to eat a ketogenic diet. Although protein can be used for gluconeogenesis, gluconeogenesis is triggered by demand, not by an excess of the raw materials. Proteins, whether ingested or already present in the body, can be disassembled into their constituent amino acids, and the body produces various enzymes for the purpose. The amino acids can then be reassembled into other proteins as needed. In the case when the body is overloaded with protein, the amino acids can be further broken down, and the unneeded nitrogen excreted in the form of ammonia. In fact, @richard just did a post on this very topic a few days ago in the Science forum. Bear in mind that too much ammonia in your system can be toxic, so that is a reason not to go too far overboard with protein consumption. Richard discusses just how much protein in the diet will lead to ammonia toxicity, and apparently the limit is quite high.
If you do a little reading on these topics, you will learn that once fat-adapted, the body has very little need for glucose, except for certain neurons in the brain that are too small to have their own mitochondria, and a couple other organs in the body. By and large, however, the brain does better on beta-hydroxybutyrate, because too much glucose causes insulin resistance, and insulin resistance makes it difficult for insulin to penetrate the blood-brain barrier, thus starving the brain. This is the reason for the mental sharpness and sense of well-being that people often feel on a ketogenic diet.
Dr. Georgia Ede and Dr. Peter Attia have done excellent blog posts dealing with these matters and citing the relevant research. If you check the Low-Carb Breckenridge 2018 thread, you will find a link to a lecture Dr. Ede just gave that goes into these processes in some detail.