On Sat, 9 Jun 2012 12:12:12 -0400, "Jon" wrote:

The right directional signal on my girlfriend's car doesn't work.

No problem. Just tell her to make 3 left turns instead of a right
turn until you get it fixed.

When you
turn on the right directional signal, both the front and back directional
light turn on but don't blink.

Since you didn't bother to disclose the maker and model of her
vehicle, it would be difficult to determine if the flasher is a
bi-metallic thermal flasher, or an electronic flasher. If thermal,
such flashers cease flashing when a bulb is blown, has too small a
load, or is presented with a high resistance connection. They also
have the irritating habit of the contacts welding closed, which I
think (not sure) might produce those symptoms. Same arcing problem
with vehicles that have flasher relays.

They just turn on and stay on. The flashers
work ok. The left directional signal works ok. Any ideas on how to fix it?

Sure. Clean contacts and connections (steering column switch, bulb
connectors, flasher connector, relay). Replace everything (bulbs,
relay, and flasher). Whatever you do last, is usually what fixes the
problem. My wild guess would be a flasher relay as in:
http://www.youtube.com/watch?v=KlVSNX_NaOs

I thought it might be the capacitor

Probably not as it's the same capacitor on the left turn circuit.

but the 4-ways work ok and the left
signal works ok. Could it be a fuse? The switch? What would cause this
behavior?

Not the fuse but mighte be the switch. I'll bet on the relay.
Reminder: Make and model of vehicle.

Jon
--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558