Originally Posted by
MightyLegnano
its actually better with the cap than without it. I know it's weird but it seems the led makes the whole cap glow like a small sun

I will make a video during the night to see it in action
If the glow is what you want, I do like your whole idea and simple design. The intermediate "on" with the reed switch is clever, making your battery last longer.
I mentioned it as an FYI. I'd rigged a lost light lens once with a red deodorant cap (it was the right size) and it did glow, but it just wasn't as bright.