You description of the problem is confusing to me, bu the statement in the title
"first signal finishes second signal starts"
suggests to me that you might want a "merge" block. This is exactly what the merge block was designed for.
This block accepts two inputs and outputs the active input. There are two requirements;
Both input signals must be the same type.
Only one signal can be active.
If this is not right, please clarrify what you are looiking for.