What is the brief estimated lifetime for the visible phase of a planetary nebula?

About ten thousand to fifty thousand years.

A defining characteristic of planetary nebulae is their extreme brevity as observable phenomena when viewed on a cosmic timescale. The entire luminous phase, beginning with the initial mass ejection and ending when the gas cloud has expanded to a point where it is too diffuse to glow visibly, lasts for only a relatively short astronomical period, estimated to be in the range of ten thousand to fifty thousand years. This ephemeral existence is much shorter than the preceding main-sequence life of the star, which might span billions of years, explaining why, despite their expected vast numbers in the Milky Way, they are not always easy to locate.