The currently accepted model of curiosity is that of Litman. It describes curiosity as a sort of motivating factor:
Curiosity as a feeling of deprivation (CFD) reflects feelings of uncertainty and tension that motivate information-seeking and problem-solving behavior.
Now we only need to establish a link between motivation and emotional intelligence. In this study, scientists found a link between the two, but came to conclusion that:
equation modeling indicates that motivation is not a factor of emotional ntelligence but that it is related to the construct particularly through the regulation of emotion and the appraisal of others’ emotions
Edit based on more updated study:
Before we proceed further, I tried to find further proof that curiosity is indeed a motivation. I found confirmation of that here, which categorises curiosity as an intrinsic motivation.
Back on topic, Here is an invaluable resource that I found thanks to mrt: The Psychological Construction of Emotion - Edited by Barrett and Russell
The entire chapter 11 is relevant. It contains lots of relevant citations too (Specially the works of Panksepp). I can't quote all of it because fair use has a limit. I will just post a glimpse:
In view of the clear evidence linking DA transmission to aspects of
motivation, what does this say about dopaminergic involvement in emotion? Is DA irrelevant as an ingredient in emotional states? Not necessarily.
Burgdorf and Panksepp (2006) suggested that ventral striatal mechanisms
are not related to “pleasure” or “consummatory reward” in the traditional sense, but instead are involved in anticipatory or appetitive energizing effects of stimuli.
The book establishes a difference between hedonic "liking" and dopamine-induced "wanting". [ Dopamine has been linked to pleasurable simulations as well as aversive stimulations ] Depressed people do not lose their appreciation of pleasurable things like tasty food (quoting the book here), but find no energy in their pursuit of motivational stimuli, exertion of effort, and motivational anticipation.
In conclusion: I would like to propose that being curious is similar to being a foodie, or adventurous. Not sure about lexical term, but there seems to be a need to differentiate between core emotions and their drive.