Eight years later; I have that phenomena om my 1992 XJ40 Daimler. For a right turn the ticking begins at normal rate but after a couple of seconds the ticking speeds up, same style as on older cars
when a bulb is shot. But in this case if I go outside and take a look both front and rear lamps flash at the normal steady rate.
So, probably the circuit senses a difference in resistance of the bulb compared to the left side bulbs and tries to falsely tell me about a bulb failure.
I assume if I change to new bulbs things will return to normal.

 

Glad you got it fixed! What was the problem? I had a side marker out which bothered me for a little while, but I figured out that those were supposed to be lit.