Is it tied into the turn signal circuit? I can't remember if the parking lights are on the Subie, but I know I experienced a bit of weirdness on a couple of Imprezas getting race prepped. The turn signal circuit passes through the hazard switch, so if the hazard switch is removed then the turn signals don't work. On one car we just jumpered a couple of pins to get rid of the hazard switch (maintained the turn signals). On the other car the hazard switch went back in.
So, it might be worth inspecting the hazard switch. I don't think that's it, but I mention it since I know the circuit is tied in and might cause some weirdness if the switch failed.
When you say the right side won't turn off, you mean EVER (as in any time the battery is connected) or do you mean with the key on? The other thing to check is the park lamp switch on top of the steering column, that's also linked to the parking lamps. If you flip that switch the park lights will be on all the time, even with the key off and removed, as long as the battery is hooked up. That might be a likely culprit.
Of course, you should mention if you've checked the grounds, bulbs, and fuse(s)...simple stuff first.
Bryce