Electrical – Sparks from desk lamp

I think I found the mechanism: There's a small hole to insert a screwdriver or something, which kinda keeps the wire in place. One of the wires required a bit more force then the other, that's why I was confused, but this seems to do the trick:

Thanks to Tester101's comment on my question I learned about ceramic high temperature wire nuts. I ended up using these: http://www.amazon.com/dp/B0071NCSA4, for 18-14 gauge wire (the ones noted in my comment above were too large, they are for 12-10 gauge wire and didn't hold on to the wires properly).

I read somewhere that halogen lights reach temperatures above 300°C, so the plastic high temperature wire nuts mentioned above are not an option as they are only rated up to 150°C. The WAGO nuts I intended to use were also not appropriate as they are only rated up to 105°C.

While I was already in there, I also replaced the lamp holders with these: http://www.amazon.com/dp/B0055D2Y2E because the metal contacts in the existing ones were corroded.

The result looks like shown below and it works great, no more flickering or humming.

I have to say that these ceramic nuts are a bit iffy to install, probably because they don't have the metal coil inside like the regular plastic wire nuts do. In one instance I twisted too much, and the nut just cut off the wires completely. Another nut never got a good grip on the wires and fell off, so I had to toss it and use another one from the same batch. If somebody knows of a better type of high heat nut, perhaps one that does have the metal coil inside, feel free to comment.