It's been a minute since I played RCT but I regained the itch so here I am.

I am currently playing Corkscrew Follies and one of the scenarios (there are actually a couple similar to this goal) involves attaining 1,400 guests by year 3 without using any sort of advertising. So you must achieve the goal through reputation alone.

Well I always rely on advertising when the goal involves a high amount of guests. 3 years is a while, which is great, but I never get past 1,200. What exactly is the formula for bringing in a high amount of guests with using advertisement?

I keep my entry fee low, most rides are very cheap and lower them as they age -- RCs when they're first built are reasonably priced. I have a mix of Gentle, Thrill, and RCs; perhaps I don't build enough coasters cause they're costly and take time. I also constantly keep an eye on Guests' Thoughts and adjust accordingly.
My current attempt I'm trying to add more scenery and keeping the paths extra clean. But I'm in early Year 2 and only have 550 guests, which is brutal. I'm thinking about making the entry fee Free, but I'm a bit low on cash at the moment. And I'm considering lowering Gentle rides to virtually no cost.

Any advice or direction to another thread (I looked but may have missed something) would be greatly appreciated.

Build more rides and rollercoasters is the only advice i can give you.
Maybe if you also try to get rewards like safest park, best food varierty and some best toilets etc. reward could increase your guests.

The game itself doesn't explain it, but there's a limit of guests you can have at a time, known as the soft guest cap. It increases with the more rides and stalls you have, with each type having its own number. Advertisements temporarily override that cap to a slightly higher count.

Further explained here: https://www.youtube.com/watch?v=viZC2WHv8As

Very interesting. Thank you for sharing this link

Yep. Every ride you place raises a cap which allows guests to keep flowing. Even the bathroom puts a few more peeps in your park.