True, but if you want even better option for daytime traffic, use a bright shirt and helmet. White/yellow/hi-vis is very easy to pick up in traffic. You could say it actually works as a reflector for sunlight. That being said, flashing lights are pretty good too, especially on cloudy days and around dusk/dawn.

Sounds you have a fake reflector there. Some cheapos don't actually have the correct prism structure underneath, but are just fancy pieces of red plastic. I have one of those in my cheap led tail light as well, it's a big red glinty thing, but has absolutely zero reflection even with a good flashlight right at it. If it's a functional reflector - even one in your clothes/shoes - it definitely will glow when you shine a flashlight at it indoors.

Which reminds me, those reflective pipings on sports clothing can be surprisingly good as well, in dark conditions. No need to go all hi-vis vest if you don't want to.