A propensity toward rational thought helps a lot. The educational process is designed to weed out the worst offenders lacking that skill. That is why you get Calculus up front and perhaps 50 students will sign up for the class and maybe fewer than ten will complete the class successfully. That is one of the “filter” classes. It weeds out those without the thinking skills required to be an engineer.
If you plan to go into mechanical engineering, then you really need the ability to think in five dimensional motion pictures. That is the three normal dimensions, plus speed and acceleration. If you go into some branches, then you need to add a sixth dimension to your thought process, which is dimensional changes due to temperature changes. If you see a structure, then in your mind you must also see the load path with all its vectors, fully understanding where they go and what they do. You will need an intuitive feel for how the structure will begin to fail and which failure mode is involved, and then develop the ability to verify your intuition with analysis.
The smartest and best engineer is worth nothing if he/she cannot communicate these ideas to those with less understanding of the subject matter. So you will need to write well, and be able to stand up before a group of people to present your work. If they don’t understand what you have to communicate, then all the other work you have done is for nothing and you have failed. As my dad taught me as a child, if someone does not want to read what I’ve written, then they won’t and I would have failed to communicate my ideas in writing—and would therefore essentially be illiterate.
I can only speak well for mechanical engineering requirements. I’ll let others speak for their fields.