Alright, so I just downloaded "Stare too long", and let's see what I can learn from it....

Okay, so the song has a rhythm acoustic guitar. You can approximate that tone with the bridge pickup and an acoustic simulator pedal (but you'll want to try different pickups than just the bridge - maybe in your case the neck pickup might work out better, I think it depends on the pedal and how your guitar reacts with it). Also, pull down the volume on your guitar a bit, too, you don't want to push a lot of volume for this sound.

As far as the electric goes, it sounds a bit like the guy is using a slide! I would try something like the following - volume all the way up on your guitar, roll back the tone just a bit, and either pick the middle or neck pickup. Get either a "blues" distortion pedal, a tubescreamer, an overdrive pedal, or a distortion pedal that cleans up very well, ie a DS-1. On your amp, put the bass below 5, the mids above 5, and the treble as high as it needs to be to be crisp without sounding harsh. You may need to futz with the tone/eq controls on your guitar and pedal to get the exact tone you're looking for, but gain should only be as high as necessary to get a bit of sustain out of your sound.

Saul