Getting into a mathematics master's program from engineering? I'm sorry if the question is not of the kind usually dealt with in the website. Honestly, I'm looking for a personal advice and/or real-world experience to help me figure what should I do.

My question is whether applying for a master's program is a good idea? or not? Given that I have no deep knowledge in mathematics, except for some engineering level linear algebra and calculus.

More details about me: I'm an electrical engineering (EE) graduate with a B.Sc. and a M.Sc. in power engineering. Although I finished my degrees with high grades and a strong resume, I didn't ever feel a thing for EE to be motivated enough to go after it in my professional life. On the other side, I always enjoyed math both in high school and college, and by "enjoying" math I'm not just talking about ordinary problem solving but mathematical stuff including defining mathematical objects, theorems, proofs and so on.

For me, the good thing about mathematics is that I always felt an aptitude for it. I get it naturally and in a joyful way. In many cases, at first sight, I feel the solution or how to get that, in a strange abstract way. During my entire education, I have always had a closer connection with my mathematics teachers/lecturers. The problem in college was that the level and depth of mathematics courses in engineering programs (even EE) was too little to feel satisfaction. Therefore, I am considering pursuing mathematics itself.
"Force = Mass * Acceleration."

You appear to be worried about your inferior "mass." What you may not realize is that you have superior "acceleration" to compensate, probably bringing up your "force" level to at least average.

I entered a math-oriented PhD program with someone who had only one year of calculus, but whose "acceleration" you remind me of. Within a year, he equalized in "mass." Then his superior "acceleration" took him to the top of the class.

The same could happen to you, if you have the natural gifts and "bent" that you say you have. Your engineering gives you enough "background" to get in the game.