Post History

I add my answer here because I think the other answers are incorrect or irrelevant: namely, the answer of Andy is nice after he has redrawn the schematic and changed the problem, answering to another (actually more interesting) question. He has furthermore assumed the line is coaxial, which is most probably not the intention of the question. 

The answer of Olin seems to me incorrect, or at least misleading: even if the two lines were very close, inducing a strong coupling, the lamp will certainly not glow continuously, but very briefly, until a continuous regime is reached. If the power supply were not a battery, as indicated by the schematic, but an AC supply of sufficient frequency, things would be different and far more complex, as we would have to take into account both the direct coupling and the continuous regime. This could be a very interesting high level problem.    

As for the original question, the answer is: the lamp _could_ have a very brief almost instantaneous glowing, if the current provided by the battery is huge, because of the tiny inductive and capacitive coupling of the wires (assuming they are not coaxial wires). But only after 1s, the time needed by the speed of light to reach the lamp via the wire, will the lamp glow more or less continuously, until a constant regime is reached after several reflections; then it will glow uniformly. 

Actually, that's not right: the electric wave do not propagate at the speed of light in electrical wires, even not in coaxial one; this is obvious for ordinary wires which own some inductance, but is also true for coaxial wires where the inductance is locally canceled by the capacitance at high frequencies. The telegrapher equation says that the velocity of the electric signal is a fraction of the speed of light (e.g. 90%). So, the lamp will begin to glow continuously somewhat after 1 s.  

My impression is that this question was created to illustrate one aspect of the electrical propagation, and was very badly thought and asked.