Neutral Spanish isn't a separate variant, so much as a separate register of the language, though. It's really just a thing I hear native speakers say when they don't realize that educated speakers from their country do, in fact, still have an accent, but it's more just down to vocabulary choice, rather than some major change elsewhere. Like, an educated Dominican isn't going to call a bus a guagua and they'll probably enunciate more clearly than they would in casual conversation, but they're not suddenly going to start using vosotros and distinción when they speak.
Whenever I hear a native speaker talking about Neutral Spanish, it's invariably followed by why I should try to speak like people from their home country, and that people from elsewhere don't really speak proper Spanish. It also tends to correlate pretty well with people telling me, "Yo hablo castellano, y por eso no puedo entender lo que dicen las personas plebes, ya que hablan español." for a nice dose of Latin American classism.
If you learn something too region specific, usually doesn’t.
My experience has been more that learners tend to not realize that certain things they pick up aren't universal, and/or that they're only acceptable in certain contexts, and then unwittingly pepper their speech with words and phrases from one country that are unknown/unacceptable in another, or use very informal/vulgar language in formal settings. Like, if I curse around my wife the way I would curse around my Mexican coworkers, she's scandalized by how vulgar the profanity is, and if I told my Mexican coworkers I had a fuinfuán in my backyard growing up, rather than a columpio, there's nearly 100% chance they're not going to have any idea what the hell I'm talking about.
And the Lamy ballpoints can finally have a decent ink, now that they're making them with the Jetstream ink. Pretty sure it's a Japan exclusive for the moment, though.