I had a strange problem with the directional signals in my 1984 XJ6 Vanden Plas after I recently got it running again, with the replacement engine, last month. For some reason, every once in a while both green indicators on the dash would light up while driving. Selecting a left or right turn on the directional signal stalk and then returning it to the center would temporarily fix the problem until it happened again. I removed and replaced the flasher a couple of days ago and so far so good.
I will be driving that car up to Los Angeles tomorrow for the JOCLA JCNA Concours on Sunday, so that 200 mile round trip will be a good exercise of the directional signals, as well as the rest of the car, after it sat for about 3 years awaiting a replacement engine.