Emotional intelligence (or competence) is highly non-verbal. In my personal path I've tried impro, biodanza, and some variants of therapeutic theater. Biodanza for me was the hardest but also the most rewarding:

https://en.wikipedia.org/wiki/Biodanza

It's difficult to explain exactly what it is, but during the sessions you don't speak, you communicate with other people through your eyes, touch and your movements. There's too much personal contact to recommend it in these virus-loaded days, but if you're the kind of person who has difficulty reading people and you're kinda stiff, this most definitely helps.