When I first built a reading light for my plastic piano (using a strip of LED tape in an aluminium channel) it only had an on/off switch, but after a short while I realised that sometimes the light is too bright (it got used mounted at different distances from my sheet music, depending on where I was playing), so I made a dimmer circuit for it.
You can get ready‑made solutions, but there was two things I didn't like about that idea: They're too big to fit into where I wanted to put it, and they use pulse‑width‑modulation (PWM) which flashes the LEDs on and off at a very high frequency. If the modulation frequency isn't high enough it can produce noticeable flickering effects to the human eye. Or an un‑noticeable flicker, but some people feel another kind of disturbing sensation that can be quite painful. And often does produce annoying strobing effects to video cameras. It's also possible to introduce squealing noises into audio circuits if they share a common power source. And can interfere with infra‑red remote control signals. There's a bunch of things to dislike about PWM light dimming, particularly with LEDs.
Instead, I opted to to use a voltage‑reduction method, which produced a reasonable range of dimming control to 12‑volt LEDs with no flickering at all (because they're always on). And rather than any complex design, I simply used a series of ordinary 1N4007 diodes with a 12‑position rotary switch picking off a feed between the junctions of several diodes, including positions for fully‑off and fully‑on.
The dimming works by diodes having a voltage drop across them (typically 0.6 volts for silicon diodes, but this differs for various types of diodes), and by varying the number of diodes in series you get an adjustable voltage drop, giving you an adjustable amount of dimming.
The diodes were soldered directly onto the switch terminals, with the whole thing placed in series with the DC power feed to the LEDs. I'm using around a metre of LED tape that draws around 1 amp, well within the specs of the diodes and switch that I used. It's a simple, cheap, and robust, design that works perfectly fine for me.
NB: If you're soldering up a circuit following that diagram, remember that when you're looking at the back of the switch contacts, it rotates the other way around (do it as a mirror‑image of this drawing).
The dimmest position is little more than candle‑light levels, which is enough to see where something is in under subdued lighting to avoid accidentally hitting it (using it like a safety light at a gig), or to be able to look at the light while you adjust things without staring into painfully bright light. There's some steps which provide enough ambient lighting to help someone who can virtually play with their eyes shut, and some comfortable bright reading‑light levels.
Of course that will vary with the particular LED tape being used, but I started off buying something that provided good bright reading light from a fair distance above what I'm looking at. 12 volt LED tape that's about 1 amp per metre is probably a good choice. For lower brightness LED tape, that won't light up with so‑many diodes in series with it, you could have a rotary switch with less steps in it and fewer diodes.
At home I use this with a 12 volt wall‑wart power supply, but when I take my piano to gigs I run it off a 12 volt rechargable gel‑cell battery (which will last for a few hours).