What does it take to make an authentic Geocities experience? Where have past attempts fallen short? Why is Neocities thriving when other attempts at the aesthetic and feeling failed so badly. I'll tell you what I think. Geocities was more than just tacky gifs and tiled backgrounds. When attempting to recreate the Geocities experience, the look is the easy part. You also have to put thought into other parts of the whole shabang.
The language used, what people were interested in at the time, the political climate, and of course, what people actually put on their sites. A lot of the earlier sites were really good ways of knowing what was going on with the people creating them. People also talked a lot about non-digital hobbies. Because that's what everyone had. They wouldn't put "browsing social media" in their interests, because there was no social media to browse! They talked about horse-riding, arts and crafts, their pets, trainspotting, movies, books, frog ornament collecting, that kind of stuff! You also have to take into account the fact that the kinds of people making these sites were giant nerds, because only nerds used the internet enough to need their own website. (Not that it's difficult to find nerds on Neocities!!). Of course, you can still talk about social media, but I recommend talking about your hobbies outside of the digital realm.
From my 'research' on Reocities, I found that one thing that was super popular on Geocities was poetry. Some sites had whole sections dedicated to the stuff. And it didn't have to be amazing, just whatever came to mind! It was an easy art form in the early days of the web, when most people didn't have access to art programs, and didn't feel like putting the time into writing much. You can just sit down and write a poem, just like that. Of course it takes effort to make good poetry, but we're talking Geocities quality here.
But back to the topic of Geocities aesthetics, I feel that there's one core thing people are getting wrong. People say "the more GIFs, the better" when it actual fact, most sites tried to keep it subtle with the gifs, because they took a while to load. If you go on GIF heavy sites from the time, a lot would have some text at the top, saying something along the lines of "Give this page 5-10 minutes to load" because they took forever to load! It's about quality, not quantity. If you have a good GIF, use it! But if it doesn't fit, or look good, don't! Plain or tiled background with Times New Roman text, is the best way to start.
Now, the reason I feel that Neocities is working is simple. They can see that Geocities was more than an aesthetic. The sites that update regularly and fill their site with their hobbies and interests are far more true to the soul of Geocities than a site that finds some gifs on Gifcities and links to their Tumblr, and leaves it there.
Neocities is special, especially in the big, cold internet of the now. It's a little treasure, filled with interesting people and original design. And I freaking love it!