If you cannot change the speed of the "interval" between the intermittency, then you got an issue on the switch on the lever, or stork as you call it :-)
This assuming the other speeds (fast wipe) are working, then the relay should be fine (without that would not work at all).
You can remove the shrouds (they are a pig to refit) and clean up the electrics on the stork, I do not recall how easy is to take it apart (I had to do the left one years ago it was fairly easy) and clean up the contacts, otherwise I would try another stork from a breaker, is an easy replacement and I do not think very expensive.
Bit of trivia, very few cars have a variable speed setting for the intermittent wipers, read somewhere it was because of a patent issue, so most automakers looked for other options (before the dreadful sensor-driven auto wipers). Pity because is a great feature to have, very useful.