What instrument is this?

[VirusDumb]

What do they play from 0:59 to 1:17

[Needfuldoer]

Sounds like an electric guitar through a flanger to me.

 

 

[mr moose]

Definitely a guitar with effects,  Was listening through cheap buds so can't be 100% but I'd say a flanger (as mentioned above) with a little reverb and low end roll off (but the roll off could be my earbuds).

[Ripred]

Some kind of guitar with either flanger, phaser, possibly a chorus effect with rapid moving phase time something along those lines

[Guest]

The effect is probably applied with a device called a stomp box. 

 

You can add echo, distortion, and more like flanger with it. 

 

I was going to start with reverb, but it could be an adjustment of flanger. 

It's also possible they used multiple effects at once like using flanger and reverb. 

 

Can't say for sure unless there is a wiki page on the song. 

[Beerzerker]

Modeling amps (I have two of those) can do it too, probrably a combo of a box and a modeling amp.
It does sound like "Flanger" is part of it with another effect applied too, sound like it could be a "Chorus" sound effect along with it to produce that sound.

I have such an amp and it can make some interesting effects, depending on how you tweak it. I don't have any real effects boxes for things like Chorus, Phaser, Flanger or stuff like that, just a Boss OD2 and "Swollen Pickle" fuzz box is what I've got.