After selecting a constructor or method completion and editing the resulting document, it should be possible to re-display the parameter information by initiating the same completion proposal just after the opening parenthesis or comma in the argument list.

The Java editor displays this as such:

NOTE: CompletionNodeFinder.createContextForCallContext is the start of this process. It is working fine for constructors but not methods (at least ones without an object expression). Then GroovyJavaMethodCompletionProposal is not setting context information position for this case (first return statement in computeReplacementString(). Lastly, org.eclipse.jface.text.contentassist.CompletionProposalPopup.insertProposal circa line 1000 is not causing the context information to be displayed for some reason.