Faulty turn signal

Hi,

One night, while parallel parking I heard a snap (or a "heavy click")
from inside the steering wheel column as I turned the wheel to guide the
car into the parking spot.

Soon after, my car, a 1997 BMW 3 Series Touring, developed a weird turn
signal problem: the right-rear won't flash anymore, while the
right-front and right side repeater flash at what seems twice the rate
(complete with matching "twice-as-fast" ticking from the turn signal
stalk on the steering wheel column).

At first, I thought it was the bulb, but the next day, I tested the
lights before driving off, and all four hazards, as well as the right
turn signal worked properly. However, during driving, the problem
manifested itself again. Now, a few days later, the problem is
persistent, i.e. the hazards won't light up the right-rear signal
(activating/deactivating the alarm doesn't either). And when I use the
right-turn signal, it flashes (and clicks) at twice the frequency.

Any idea what the problem might be, and where I should look first?

Thanks,

-- Peter