That being said, I think it's kind of becoming a dying art to orient yourself by compass and cardinal points. Most people have a hard time thinking in cardinal points and don't seem too interested in fixing this. But that is a shame since directions such as "go right" are too relative to your reference point to eliminate confusion.
Satellite dishes can be a very useful directional reference in many urban environments. Here in the UK the overwhelming majority of dishes are aimed at the Astra constellation, so they indicate an azimuth of rougly 155°.
Because anybody would care how one proceeds? If it's meant to not seem tourist to pickpockets and the like, those can tell anyway...
I wore it on my keychain - and I still do! Doesn't come in handy as much since I know where I'm going but it's nice to carry around.
(It didn't help that cars were on the opposite side of the road too, so my baked-in "look left when you approach a road" response was suddenly not so helpful.)
My understanding is that it tells you how parallel you are to the magnetic field lines.
I don't see how that helps you find the stairs. All I can see is that if you lay it down on some steps, it will tell you whether it's pointing uphill or downhill.
Is that not correct? Do the magnetic field lines in a tube station somehow point towards the exit rather than the north pole?
I've got a Westclox Baby Ben glow in the dark wind-up alarm clock that I've had at least 50 years . 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 , 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  work?
CMOS sensors can detect gamma particles. If you have an android phone there's an app that actually works (assuming you follow the calibration steps properly). Apparently Radium mostly emits alpha particles so I'm not sure how effective this would be.
If you are thinking about buying an actual geiger counter make sure to get one with a working probe assembly. A lot of surplus geiger counters are sold without the probe assembly with is the expensive part and the thing that wears out. The probe assembly also needs to be properly calibrated.
I'm amazed by the simplicity of the solution, it's a brilliant idea.
Same for the buttons sewn on the uniform, and the other everyday objects that turn into a compass, I love how they are hiding in plain sight.