Will the NES Zapper light gun work on a CRT HDTV?

The NES must do the following to "read" the zapper:

1. Wait until next frame starts
2. Make the screen black, except for a small area where a target is
3. Read the zapper to see if it's detecting light
4. Wait until next frame starts
5. Make the screen completely black
6. Read the zapper to see if it's not detecting light

If it detected light in both step 2 and 5, the zapper is not pointed at the TV set and the program should count it as a miss. However, if light was detected in step 2 but not step 5, then the program should count it as a hit. This is why the screen flickers in Duck Hunt, and the duck sprite is replaced with a solid white sprite for 1/60th of a second, when you pull the Zapper trigger.

TL;DR: It should work on any TV if the contrast and response time of the display are good enough.