Yes, agreed: Engineering Manager. I often make this mistake because English is not my first language, and I confuse "engineer" with "engineering": in both case

Yes, agreed: Engineering Manager. I often make this mistake because English is not my first language, and I confuse "engineer" with "engineering": in both cases it sounds to me "a manager who manages engineers", not "a manager who is an engineer him/herself". Kind of like a "Product Manager" is a manager who manages the product, not a manager who is a product!