So I was reading the news about a Dead Space remake and much like the rumored The Last of Us remake before it, my initial reaction was: "This game isn't old enough to get a remake!". To me PS3/360 games still look and play fine today. Maybe it's because I've never been that much of a graphics whore but I don't see the appeal in remakes of 10-12 year old games. 

On the other hand, I thoroughly enjoyed the Resident Evil 2 and Final Fantasy VII remakes and never doubted their relevance. From reference the gap between these games and their remakes was 21 and 23 years respectively, so it seems that for me 20 years is sort of a sweet spot to consider remakes "worth it".

What's your idea of the perfect gap between original and remake?

Well none of the early 360 games aged well (2005-2007ish) so I'd be happy with an Oblivion or Bioshock remake.
Dead Space on the other hand released in 2008 and has aged much better since devs had more time with the console tech. When the remake releases, it will be 14 - with delays maybe 15 years old. That doesn't seem so bad but not really necessary. I guess they just wanted to get away from DS3 and make a fresh start.

A The Last of Us remake sounds idiotic though when the sequel released just a year ago.

No specific time frame. The original just has to be outdated in gameplay and/or graphics so that a remake can bring the game into the modern age of games.

Both the original versions of RE2 and FF VII look and feel archaic and outdated.
The Last of Us and Dead Space still look great (can't comment on how they play, never did so), they don't seem to need a modernised version because they didn't age enough for that.

Well, not many remakes are ever "warranted".
I would say most remakes need a bare minimum of a console generation (5-8 years), but two console generations (10-14 years) is usually a better idea.
If The Last of Us didn't get a PS4 remaster in 2014 (only a year after its PS3 release), I could understand remaking it already in the early 2020s. But the PS4 release in particularly has aged very well, especially when you play it on a PS4 Pro or PS5.
Xenoblade Chronicles got a remake 10 years after its initial Japanese release, 9 years after the European release, and 8 years after the North American release. Considering that game was so held back graphically by the Wii, more than enough time had passed.
A lot of Xbox 360, PS3, and Wii U titles don't really "warrant" remakes yet. But the Wii, 6th generation consoles and earlier? Go for it. I'd like to see more fifth generation remakes in particular.

The only thing a game needs to be remade or remastered is research indicating there is a big enough crowd out there that will buy it if it is remade/remastered. There are entire studios that focus entirely on remaking old games so the teams that made those games can continue making new content. It gives them work/pay, gives the gamers who want those games remastered/remade satisfaction, and allows more money to go into development of new games by whoever publishes it. Win-Win-Win

It needs to be at least 20 years old, and it needs to stay as true to the original as possible.

Do you dislike Final Fantasy VII Remake? 

I don't think there is any specific age.

But a game does warrant a remake when there are tangible benefits to doing so, not just from a visuals perspective but quality of life gameplay updates thanks to new technology.

Alright, you got me with that sentence, it's a nice way to put it. 

I suppose there no specific time frame for this, but the older the game is the more sense it makes I guess?

For me, personally, I agree that the ps3/xbox360 games are "too new" and remaking (Not remastering) them feels off. The gens before that (ps2/xbox/gc) dont give me that impression because those are games that look dated today, at least graphically. The RE Remakes or the Spyro trilogy are very well done and theres a VERY noticeable jump in visuals between the originals and the remakes. And remaking 2D games is something Im always on board with because even if they stay true to their source material they will always feel like new games, which is something I feel all remakes should be like. Case in point Trials of Mana or TLOZ Links Awakening.
But none of that matters, because they havent remade Chrono Trigger, so really, whats the point?