After a little more testing
-A privateer needs to be able to reach the city without having to pass through one of your cities or forts
Example
In this example the privateer can reach Uppsala directly but cannot reach Nidaros without passing through my own city or forts as such only Uppsala is affected.
Interestingly it seems
you do not need to know of a way to reach the city, just be able to (tested with long continent and without exploration)
I think we can call this the
open seas rule
**Edit Privateer blockades can pass right through sea ice tiles regardless probably same reason as the infinite ice canal is possible with forts (ice being over seawater).
-If a Privateer actually cuts the trade network it still gains

, to me this seemed weird at first, how can it make gold if theres nothing there to get!?.
After a little fiddling around I found that the

you gain is directly linked to the maximum
possible trade routes also shown by the above example in that I am gaining 8

while there are only 2 Viking cities.
I had given Ragnar currency, Great Lighthouse, Castle, Citadel and other things in Worldbuilder. In total it allowed 8
trade routes.
I bumped up population later to test how this affects the situation.
Picture
Here each trade route is worth 4

to the city after modifiers.
With 8*4=32 I can be pretty certain the

gained is equal to the total of all possible
trade routes after modifiers regardless of if they exist.
I tested this by making Nidaros large enough to generate 5

per turn per
route but only having 4
routes max test is shown
here
The above means that if you cut the trade network to a city, you still gain the same

and that

gained is independent of actual trade routes it seems. It would seem though that if your killing the cities population you will gain lower amounts of

over time.
Also noticed that if you sever a
trade network from another city while privateer special blockading the city you disconnect:
-When the blockade is ended (it dies or you move it) the
trade network is immediately restored the second the blockade is lifted.
-But the blocked
trade route effect on the city the privateer is affecting directly stays until the next turn.
The other largley neglected use of a privateer is blockading in the middle of 'nowhere' to break intercontinental
trade networks.
The setup
Here the two mainland cities are providing the
island city with iron, and 2
trade routes
I've only allowed Ragnar to have sailing for this, astronomy would make giving an example way to complicated, I have used this very successfully on archipelago maps post astro though.
So with a
privateer blockading between we get
this
I think it obvious that it affects
all international trades too.
I attempted a little example but I can''t get 2 AI's to trade a resource for a resource
The scenario
The trade
For a privateer at peace this would obviously block the trade.
Using a frigate I declared war on Ceasar the wheat still went to Ragnar, It was however blocked when I declared on Ragnar. The privateer however acted like the frigate toward whoever I warred with, but also prevented trade the other way as a privateer.
I wish I could test the effects on a, say iron for copper trade, but the AI won't seem to trade anything for another resource when I try

. I want to see if it will physically cancel the deal and put an end to the "We appreciate the years you supplied us with resources" diplo boost. All though the fact that the Roman city Antium got its wheat back when the blockade stopped it seems promising.
In certain cases it may be possible to block effectively all intercontinental trade using privateers that are nowhere near rivals cities! In theory this could be abused, you can actually channel the blockade to make
your cities the only ones that can be traded with

. How doable/effective this can be though I have no idea.