Transistor not giving expected voltage

I'm using a 12V power supply for powering my Arduino Uno board. I want to make a lamp blink that's apparently rated for up to 125 V (it lights enough under 12 V, but it's way too dim under the standard 5 V). Since the board's output pins' HIGH value is 5 V regardless of the power supply, I figured I'd use a 2N222 transistor as a switch to switch the 12 V to the lamp.

So I have the collector connected to the Vin pin, the emitter pin connected to the lamp, and the base pin attached to a 10K ohm resistor and then one of the output pins.

The problem is whenever the output pin is HIGH, the voltage read across the collector/emitter is still 5 V (a little less actually). Why is this? I figured the transistor would act as a simple switch and turn on the 12 V across it...?

Connect the emitter to ground. The base through the resistor to the Arduino pin. The bulb then connects between the collector and the +12V. Then read the emitter to collector voltage. It should be close to what you are looking for.

I assume you are using a 2N2222 transistor.....

Hmm, I don't understand fundamentally how that's different from my circuit, and the multimeter still read 4.5 V, but the light works now!

You had an emitter follower, what was needed was a common-emitter circuit. Emitter follower cannot amplify voltage, only current. Google these terms for more information.

4.5 V is too much, decrease R from 10 k Ohm to 1 k Ohm or so. Btw, transistor rated for 0.6 A max, what kind of lamp do you have, I'm afraid it take more current than 0.6 A

The "lamp" I'm referring to is actually an illuminated pushbutton that says "125V MAX AC/DC, 3W MAX" on the full voltage unit. The light lights under the 12 V, albeit somewhat dimly. I know transistors can amplify so is it possible to somehow amplify the 12V to make the lamp brighter?

Yeah, I just looked up the bulb online and it states it a 28 V bulb. And I kinda figured transistors didn't have magical voltage-increasing powers, but thanks for confirming it. :)

Thanks for all the help everyone!