Passenger daytime running lights/low beams not working 2005 WRX

It's the dimmer switch. Which is called the multifunction switch or turn signal switch. Just because it clicks, doesn't mean the it is working properly. If you click and the high beams come on, then click it again and have no low beams, replace the switch. Daytime running lights are controlled by the Body control module.

This is usually caused by a failed front control module as this unit controls the lighting on the vehicle!
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DAYTIME RUNNING LIGHT MODULES CAUSE A PROBLEM LIKE THAT

Headlamp relays are most always in the engine compartment in one of several power distribution boxes. It could be the dimmer switch, DRL module, or both bulbs. This happens because the lights are so bright, one low beam has burned out, and goes unnoticed until the other one burns out also.
Daytime Running Lamps (DRL) use the low beam but at a reduced power, which shortens their working life. Hope this helps.

The blinking light is telling you that you have a headlight out, if you look the service light should be coming on when the light stops blinking.
Replace the head light and all should be fine.

put your old headlites back in and try it, if drl works the the resistance in the new lites isn't compatible with drl relay

Look for the relay for the head lights,it may be bad.Also look for a bad ground.And check the bulbs too.

check the head lamp dimmer swicht

check all grounds

the click you are talking about is the high beam relay.
you nedd to get a tester or voltmeter and check the sockets for 12v.
there has been instances where both low beam bulbs went at once.
do the daytime running lights work?
if not,supect the daytime module...it is also wired into the parking brake.
if you put the park brake on first,then start the vehicle,the dtr do not come on