Purchase a Harbor Freight Multimeter $4.99 or go wild and buy the $20.00 version.
There is a Harbor Freight store near you.
To Check the bulb.
1. Unplug the bulb
2. Setup the multimeter as an Ohm meter
3. Place the meter leads on each of the disconnected
4. Check both the "new" and old bulb. Sometimes the new part is bad.
5. You should have a small Ohms number if good. A bad bulb will display an OL on the meter, just like when the leads are not touching anything.
Another way to do this is swap the left and right side bulbs to see if the working bulb also works on the other side. This method is not as much fun as playing with the meter and sometimes leads to two broken bulbs. Don't touch the glass and don't drop the bulbs.
You can also test the voltage available at the bulb socket.
This is a 12 volt DC circuit for the DRL's, so use the 20 DCV setting on the meter. Change the meter to test DC Volts.
Turn on Day Time Running lights
Connect the voltmeter leads to each socket terminal, Brown wire terminal is ground so use the Black meter lead. The Red meter lead to the other terminal.
You should have more than 12 volts or battery voltage.
Sorry for getting carried away. I haven't taught my Automotive Electrical Systems class in weeks so I needed to vent.