Switching paths very late I am going to graduate this spring with a BSEE, but I have realized only now that going into the engineering industry is not the direction I want to take my life. After doing some deep introspection I realized that what I really want to do is go into academia, specifically in mathematics. Luckily, I had at least some foresight early on and picked up a minor in math. Ideally, I would like to finish the degree path that I an on and move straight into a masters program and then hopefully, eventually a doctoral degree program. However, after reviewing the requirements for acceptance into and curricula of several major math graduate programs and even the graduate program of the state school I currently attend, I am wary that, despite the amount of mathematical knowledge I have gained from my minor and what I have gotten from engineering, I am not well enough prepared for graduate school or to even get into a program.

So my question is should I still apply to graduate school despite these misgivings or would it be a good idea to switch majors/pursue a second bachelor's before I think about applying for graduate school. I am not unwilling to spend the extra time and money to do so but at the same time I am wary of doing something this drastic so late into my undergraduate career. Although one thing I am certain of is that this is indeed the path I want to take.
First of all, don't be too worried, switching after the Bachelors is not "very late" and happens more often than you seem to think.

Now for your question: I would first try to find a university/program you like to join. Maybe even more than one, in case that you don't get into your first choice.

Then, you should contact the advisor(s) responsible for this program and ask them your questions. The requirements are a little different for every program, some offer the chance to catch up on missing courses during the program, others require it before the program or don't offer it at all. Thus, we can't really give you a general answer here, as every program handles things a little different. But, as I said in the beginning, it is not entirely uncommon for students to switch paths, so most program advisors should be familiar with such cases.