A few questions...
Do you know where that "12V" wire is coming from? For example, is it "power" from a switch or something, or is it some sort of low-current "control signal" ? If you don't know what the wire is for, you shouldn't be connecting things to it... or at least you shouldn't be connecting anything that draws more than a fraction of a milliamp.
What's normally connected? The light is something you're adding, right?
Do you get 12V without the light connected? I mean, what makes you think there should be 12V there? Ort, did you connect the light and blow something, so that there's no longer any voltage there?
I was a bit evasive in my OP, sorry about that.
The light in the boot of the car is not coming on anymore when the boot is open.
I checked if the lamp was fried but it's not.
Then I checked if the switch to detect whether the boot was opened or closed was working, and it is: when the switch is pressed (= boot closed), there is 0.00V flowing to the lamp. When the switch is not pressed (= boot open), there is 0.95V flowing through. But the lamp is not coming on because it is rated for 12V 5W.
So I thought I could just use a voltage regulator to take the voltage back up to 12V and have the light work normally. Or I could make a small PCB with a 3.3V regulator, a resistor, one or two 12k mcd white LEDs and a fuse (the original Toyota lamp looks like a fuse and I'm thinking it doubles up as a fuse) and place it there so I could get light with minimal voltage and current draw.
Alternatively, I could use a ATtiny to monitor the wire for voltage and turn on the above mentionned LEDs PCB powered by a battery or two that I would change every now and then.
My main problematic is that I have very basic electronics knowledge and I don't have the tools not the courage required to take the car apart to dig up the wire and check it all the way to the (brand new) battery.
All in all it's a minor annoyance, everything else in the car is working fine, but I thought it could be a useful and fun mini-project. Thoughts?