Final answer:
The most important properties of metals in the lamp's wires are that they conduct heat and electricity well, and that they are ductile, ensuring smooth electrical flow and ease of installation within the lamp's structure.
Step-by-step explanation:
To make Talia's lamp work, conducts heat and electricity well and being ductile are the most important properties of metals in the lamp's wires. These properties ensure that electric current can flow smoothly through the wires to light the lamp, and being ductile means that the wires can be drawn into thin strands that fit into the small spaces within the lamp. Metals are also known to be malleable, which is useful for manufacturing, but it is not directly relevant to the function of the lamp when turned on. The shininess or luster of the wires is more of an aesthetic property rather than a functional one in this context.