Blue tubes need mercury
Neon gas by itself glows orange. Sign makers get blue by adding a little mercury to the tube, says the Wikipedia article on neon lighting. So a blue "neon" sign owes its color to a different element.
A bright cyan from a survey
Our #04D9FF is the neon blue from the xkcd color survey, where people named random colors on their screens in 2010. It is a bright cyan blue. Wikipedia lists neon blue three ways: #1B03A3, #4666FF and #4D4DFF. All three are deep purplish blues, far from ours.
Closer matches on this site are vivid sky blue and electric blue. Black text works well on #04D9FF, at 12.37 to 1.

