Fuse: why does it connect in parrallel with resistor?
This fuse holder has a small neon bulb in series with the resistor. The neon bulb acts as an indicator that the fuse has blown.
When the fuse is intact, the voltage across the fuse is small. So is the voltage across the neon light with resistor, because it's in parallel with the fuse. When the fuse blows it becomes open circuit, and the supply voltage appears across the neon bulb with resistor. The neon bulb lights up. The purpose of the resistor is to limit the current through the neon bulb.
Wired across the fuse terminals and contained in the plastic cover is a resistor and neon indicator that would presumably light up if the fuse was ruptured. [from Amazon product customer review]
Your fuse holder already has a resistor and neon bulb in parallel with the fuse. As the fuse is basically a near perfect short in parallel with the resistor and bulb, the resistor and bulb will have little to no current flow. It looks like it is a Brown Black Yellow resistor with Gold or Silver tolerance, which is 100K 5~10%. When the fuse blows, the resistor allows a little current through the neon bulb, lighting it to let you know the fuse blew.