Well, I've made progress. Found the online shop manual again(they moved, old link doesn't work, I found it a while ago but forgot to bookmark it, silly me) and said that a rasping noise could be caused by broken or loose parts, which I would describe this noise to be before it actually can honk. I removed the driver's side horn earlier as I suspected it to be the one with a problem, and I was right. On an impulse I just hit the horn button a couple minutes ago and it honked, but only with the driver's side horn off leaving the passenger side horn on. So, I believe that my driver's side horn has something bad in it, but why would my passenger's side horn not work with the driver's side horn on?