I think the black stripe at the top of the rudder horn balance is probably just paint. It might be a rubber protective strip, as the rudder is fabric-covered.
As far as I remember, the TKS porous metal strips are only installed on the leading edges of the outboard wings and tail plane. I don't think the fin has one.
I ferried one from Malta to the UK. It had been sitting out in the sun for a few months. After a good few engine runs and a test-flight, we set off. Traversing a cold front just south of Sicily, we started picking up some ice. I switched on the TKS system and watched, fascinated, as the ice ridges continued to grow! After a few minutes more, and following a lightning strike, I decided to turn it off. The ice stopped growing and eventually ablated after we exited the clouds. I reckon water/condensation had settled in the TKS fluid tank and so I was growing my own ice!
(About 1000 hrs on Doves in the 70s and 80s.)