Serious pen owners do the following: One cup of slightly warm water. Add one drop of washing-up detergent and one drop of ammonia. Fill pen several times, flushing it not back into the cup -otherwise you won't see when it's running clear. When it looks clear, fill one more time and leave for a while - perhaps a half hour. Then flush it. If it is clear then job done. If not then do it again. End by flushing several times with clean water, then leave to dry. I use a dish placed on a radiator.
The flush and leave is because some dried ink remnant needs time to loosen.
Ammonia. I tried to buy from the local chemist, but was refused since it is used to make crack. So I bought it from your friend and mine - Amazon. It's called Kleen Off. 500ml.