This is for Neo City, not to be confused with the similair Neo Tokyo content and issues.

Confirmed, and it's a genuine dead end — thanks for chasing this all the way to the door.

The Time Gate is behaving correctly: it stays switched off until you've finished "Andy the Time Traveler", which is the quest where Andy asks you to find the Pocket Watch he lost in Minar Forest.

The problem is that the Pocket Watch cannot drop. It's supposed to come off fourteen Minar Forest monsters — Harp, Blood Harp, the three Kentaurus, Birk, Dual Birk, Rash, Dark Rash, Hobi, Green Hobi, Beetle, Dual Beetle and Hankie — at about a 6% rate while that quest is active. The item exists in the game, and all fourteen monsters exist, but not one of them has a drop entry for it. So the quest can never be handed in, so the time machine can never be activated, so every Neo City era stays locked: all eighteen field maps, the six Nex arenas and the five boss fights including the Dunas your "Identity of the Missile" quest is asking for.

I'm adding the fourteen missing drop rows. Once that's live, take the quest from Andy, farm any of those Minar Forest monsters, hand the watch in, and the Time Gate menu will open with the eras you've unlocked.

Confirmed, and it was a genuine dead end — you couldn't have gotten through it no matter what you tried.

The Time Gate itself is working exactly as it should. It stays switched off until you've finished "Andy the Time Traveler", the quest where Andy asks you to find the pocket watch he lost in Minar Forest. The problem was that Andy's Pocket Watch could not drop from anything. In the real game fourteen Minar Forest monsters drop it at about 6% while that quest is active, and none of those fourteen drop rows existed here — so the quest could never be handed in, so the gate never switched on, so you got "The time machine has not been activated yet." every single time.

This patch adds the fourteen missing rows, copied from the server data rather than guessed: the mobs are 7130002/3/4, 7130500/501, 7130600/601, 8140001/002 and 8140101/102/103/110/111, all at 6% and all gated to that quest so they won't clutter your drops otherwise. I checked and all fourteen are actually spawned across Minar Forest maps 240010000-240011000 and 240020000-240020501, so they're farmable.

Once this is live: take the quest from Andy, kill any of those Minar Forest monsters until the watch drops, hand it in, and the Time Gate will open its menu with whichever eras you've unlocked. Note the eras themselves unlock one at a time by beating Guardian Nex — the first menu row is Year 2021, and Year 2215 (the one your missile quest wants) is the third, so you'll have to work up to it.