Is there a reasonable way to tell if an old glow in the dark thing uses radium (or some other radioactivity based lighting mechanism) rather than simple phosphorescence, short of finding a Geiger counter?

I've got a Westclox Baby Ben glow in the dark wind-up alarm clock that I've had at least 50 years [1]. I don't think that there is anything I have owned longer. It still works fine, although sometimes it needs to be slapped a little to get it going if it hasn't been used for several years. I still use it as a backup whenever I need an alarm in circumstance where an alarm failure would lead to serious, hard to deal with consequences.

Westclox definitely used radium at one time in their Baby Ben clocks [2], but from what I read they stopped in the early to mid '60s. Mine was bought around the mid '60.

Mine only glows after exposure to bright light, suggesting it is using phosphorescence rather than radioluminescence, and so should be safe, but it would be nice to check.

Would a homemade cloud chamber [3] work?

[1] https://imgur.com/4CljfDL

[2] https://www.youtube.com/watch?v=wp6Ddcc4GAg

[3] https://www.sciencefriday.com/educational-resources/build-a-...