How about...bath through 90 deg. Shower top left. Pocket door then towel rail nearer the door?
Don't really want the towel rail near the pan.....you might burn your knee. Then there's splashback etc 😬
I think there's a capacitor in there that stays charged when the light is "off". Also some clever circuitry that lets pulsed power through to keep it charged but not enough to put the light on.
Or something like that!
I'm amazed you're not making them yourself!
Something like this? They make to order:
https://www.silverapplewood.co.uk/products/solid-pine-spice-rack-5-tiers-shelves