We see these traits very clearly whenever Éowyn interacts with Aragorn. When she first meets him, her eyes linger on him, she becomes "aware" of him. Everything Tolkien writes in their subsequent interactions connotes her desire for him. She's clearly attracted to him.
Yes, a lot of people read her interest in Aragorn as her wanting to *be* him. Aspects of that are true, but that's not the whole picture. She desires his power and freedom, but she also desires him; she desires what he can offer her; she wants to be chosen, seen, lifted out of her life, and empowered by having her romantic feelings returned. She does want to be transformed, but the transformation she envisions is one that emerges from Aragorn respecting, choosing, and desiring her. Tolkien is pretty clear (especially when Faramir calls her on these feelings later) that these desires stem from both romantic attraction AND platonic admiration, and the two are inextricable from one another.
Éowyn is also very earnest. We see this most clearly when she begs Aragorn not to ride into the haunted mountain. She opens her full heart to him, sincerely shares some of her deepest emotions, and hopes that in doing so she can either convince him to turn aside from his course or bring her along. These are not the actions of someone who is cynical about love and romance, these are the actions of someone who believes that baring her soul to the man she (thinks) she loves might yet win her the outcome she desires. That's the opposite of how a cynic acts.
I understand why a lot of people want to read cynicism about love and romance into Éowyn's character arc. She's been harmed by sexism and pressed into a mold of gender expectations. They want to see her as a girl boss, someone who fights, bucks norms, and isn't interested in ~silly things like ~male desire. And like, I get where that's coming from, but she the truth is that she is. Maybe you don't want her to be or think she shouldn't be, but as the books are written, it's a defining and driving force of her character arc, and moreover, it makes sense given her cultural context and life experiences. Indeed, her desire for a romantic life with Aragorn directly precedes her desire for a romantic (in the Rohirrim tradition at least) death in battle. Tolkien tells us this directly, via Faramir:
"You desired to have the love of Lord Aragorn... but when he gave you only understanding and pity, then you desired to have nothing, unless a brave death in battle." (1)
She looked to love first, as her last ditch effort to escape the life that was confining her, and then when that did not work, she turned to death. I think a truly feminist read of these beats doesn't deny that fact that Éowyn wanted to be desired romantically, but gives it its due weight and breathing room because its a sincere and important emotional experience of a female character in this story!
footnotes:
(1) LOTR single edition, pg. 988 (The Steward and the King). I think it's very clear from this passage that love and platonic admiration are completely co-mingled in Éowyn's mind. Faramir notes that she admires Aragorn "as a young soldier might admire a captain" (my paraphrasing), but the context of the whole passage is a discussion of romantic love. Taken together with that context, this line very deftly describes the sort of romantic desire that arises when someone encounters a powerful and intriguing figure that they don't know very well.
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