Early morning is the cleanest answer
The sign is free and public, which also means the queue can form quickly. Early morning usually gives visitors softer light, calmer traffic energy, and a better chance of getting a clean center-frame photo without waiting through several groups.
If the direct line is already long, the side angle is not a failure. It keeps the star, bulbs, poles, and median setting visible while reducing the pressure of the classic straight-on queue.
Blue hour is prettier but slower
Blue hour gives the neon and bulbs more atmosphere, especially in photos that include the surrounding Strip glow. The tradeoff is more people, slower exposures, and less forgiving phone-camera blur.
Treat blue hour as a mood pass, not a quick stop. If the goal is one reliable postcard frame, morning is still the more dependable plan.
Image: Hermann Luyken, CC0, Wikimedia Commons