Ah! now I understand your issue.
When you define a Block1 having some Block1 properties and you define connectors within the Block1 IBD you want to see those connectors in an IBD of a Block2 having a property classified with Block1.
This is unfortunately not supported by EA. You can only synchronize the properties but not the connections.

What would work, is if you would define the connectors within a Block2 IDB, than you could have different Block2 IBD reusing the connectors. But this is not your use case.
What I do in this scenario, is using the property of Block1 in the Block2 as a black box having a kind of diagram link to the Block1 IBD.
Unfortunately EA does not support “Select Composite Diagram” for properties for whatever reasons, so I use the diagram Hyperlink feature.
Another idea could be to use the “Show Composite Diagram in Frame” or “Show Composite Diagram in Compartment” feature. However again you are not allowed to use that feature for properties.

There are some areas in EA where Sparx spend presumably considerable effort to implement features and then they spend additional effort to block those features for stuff which could benefit from.
It is like a company would make a car, but only allow persons with name Fred to drive it.