Everland theme park is in Yongin, not Seoul, and no train reaches the gate

There is one reason Everland days go wrong, and it is not the queues.
People plan for the queues. They read about the wooden coaster, they accept that a Saturday will cost them some standing, and they turn up ready for it. What nobody plans for is the getting there and the getting back, because the search that brings you to this park has the word Seoul in it and the park is not in Seoul. It is in Yongin, in Gyeonggi-do, about forty kilometres out, and there is no train that reaches the gate. Sort those two things and Everland theme park is an easy day. Leave them to the morning of and you lose two hours at each end.

The park is in Yongin, and the last five minutes are always a bus
Whichever route you pick out of Seoul, the final leg is a shuttle bus.
That is because no railway line runs into the park itself. The nearest station is the terminus of a local light rail, and it sits a short distance short of the gate — near enough to be named after the place, far enough that you still have to get on something else.
In practice there are two routes. The subway one takes about eighty minutes: any line down to Giheung, then the Yongin EverLine light rail for roughly half an hour to its last stop, Jeondae·Everland, then out of Exit 3 to a free shuttle that runs to the gate in about five minutes. Tap the same card you use in the city — if you have not sorted that yet, T-money card in Korea: what it is, where to buy it, how to use it covers it. The other route is a paid direct shuttle from pickup points in Seoul, Hapjeong Exit 4 among them, from around 11,000 won.

So the station called Jeondae·Everland is not at Everland. Budget the last five minutes as a separate step, and if you are running for a parade or a fireworks slot, run for the shuttle rather than the train.
The same trick catches people an hour east of here too — Nami Island: the address is in Chuncheon and the boat leaves from Gapyeong.
So what time does it actually close?

The closing time is not a number you can look up in advance
Do not copy the opening hours out of somebody else's article.
The reason is that Everland does not run to one timetable. Hours move with the season, with the day of the week, and with whatever event is on, and winter takes some attractions out of service entirely. This is why two guides written a year apart will confidently tell you two different closing times, and why both of them can be wrong for your date.

What the park does instead is publish the confirmed schedule for the coming week on its own site, and it goes up on a Wednesday. That is the number to plan around — not the one in a blog post, and not the one a booking site prints next to a ticket.
So check the official weekly timetable on the Wednesday before you go, and build the day backwards from that day's actual closing time. It takes two minutes and it is the single highest-value thing you can do before an Everland theme park trip.
And the ticket — is it one ticket?

Caribbean Bay is a different park with a different ticket
The water park next door is not part of your day pass.
Caribbean Bay shares the complex, the address and half the search results, but it is a separate park behind a separate gate, and an Everland theme park day pass does not let you through it. Combination tickets exist and are sold widely, which is exactly why people assume the standard one covers both.

So decide which of the two you are actually going for before you buy, and if you want both on one day, buy the combination deliberately rather than discovering the gate at two in the afternoon.
This is the same shape of problem as the one in Jamsil — Lotte World: four places share the name and they are four different tickets.
Which leaves the part everyone forgets until it is dark.

The last EverLine train is 23:30
The light rail you came in on stops running at half past eleven.
It runs from 05:30 to 23:30, and it is the link in the chain with the earliest cut-off — the Seoul subway lines you transfer onto afterwards are not the constraint, this little local line is. Miss it and you are looking at a bus or a taxi out of Yongin, at night, at the end of a long day.

So work backwards from 23:30 rather than from the park's closing time. Leave the gate, take the shuttle, and give yourself slack at Jeondae·Everland — the queue for that shuttle is at its worst straight after a fireworks finale, because that is when everybody has the same idea at once.

If you came on the paid direct shuttle instead, the return departure time is fixed when you book it, so the answer is on your own ticket. Read it before you get absorbed in the park rather than after.

FAQ
Is Everland in Seoul?
No. Everland theme park is in Yongin, Gyeonggi-do, about forty kilometres from central Seoul. It shows up in Seoul searches because that is where most visitors travel from, not because it is in the city.
Can I do Everland and Caribbean Bay on the same day?
Only with a ticket that covers both. They are two separate parks with separate gates, and a standard day pass for one does not admit you to the other.
How long does it take from Seoul?
About eighty minutes by subway and light rail, plus the five-minute shuttle at the end. A direct shuttle bus from a Seoul pickup point is simpler but runs to a fixed schedule in both directions.
Is the shuttle from the station free?
Yes. The shuttle between Jeondae·Everland Station Exit 3 and the gate is free. The paid shuttle is the different thing — that is the direct coach from Seoul.
What to do before you go
Everland theme park is in Yongin, not Seoul. No train reaches the gate, so the last five minutes are a shuttle either way. The closing time changes week to week and the park publishes the real one on a Wednesday. Caribbean Bay is a separate ticket. The last EverLine train is 23:30.
None of that is difficult. It is just that all five are decided before you leave your accommodation, and none of them can be fixed once you are standing at a gate in Yongin at ten at night.
So do the one thing that makes the rest fall into place: open the official site on the Wednesday before your visit, find your date on the weekly timetable, and write down two numbers — when the park closes, and 23:30. Plan the day between them, and the queues go back to being the only thing you have to put up with.
References
-
Yongin EverLine — operating hours 05:30 to 23:30
-
Gyeonggi Tourism Organization official blog — getting to Everland from Seoul
-
Everland official site — weekly confirmed operating schedule, published each Wednesday