Even if it's true that IQ is measurable and EQ is not, meaning you can't walk around with a numeric bell curve score for your EQ, that doesn't mean we don't each have a sense of gaining and losing EQ points over a lifetime.
You can suddenly have insights and understand yourself and others a lot better. Part of that just takes growing to adulthood. You gain empathy for people raising kids, by raising kids, and so on.
I think the game in both cases is to guard against losing points, which means exercise and train to stay at full potential (for you).
I believe EQ is trained by novels, movies, soaps, TV series (not all of them, just the ones that do). Also travel. Having friendships and community. EQ is developed and cultivated.
Even if we think IQ is somewhat fixed (everyone has a maximum they can't go beyond, similar to physical height and/or maximum strength), there's the question of whether we value it or not and/or have opportunities to "work out" in order to live up to our full potential.
Sometimes we're not rewarded for physical strength. Likewise, you my be stuck in a routine, not of your own making if you're not free, that has no use for your stellar IQ. Picture an Elon Musk type wasting away on a marijuana charge in Texas. Times a million around the world.
Humans deliberately sabotage their own smarts, to conform to social norms. Women have been especially so encouraged.
I'd say a polymath is someone who (a) values both IQ and EQ and (b) strives to "stay in shape" which means "round" (as in well-rounded). Life by its very nature is multi-topic, multi-subject, so the very process of staying in shape is going to take care of the poly part.