When providing traffic information to ac under a RIS I would hope that controllers give pertinent information that allows the pilot to build up the 3-dimensional picture of significant traffic. Standard traffic information under RIS should consist of:
Relative position of conflicting ac in terms of bearing (clock code) or compass points to a manoevring ac.
Distance in nm
Relative movement to subject ac. This is where the crossing left to right / reciprocal heading or suchlike comes in.
If known the level of the conflicting ac. Normally given as 'indicating FL??' or 'indicating ???ft if using SSR. If no height information is available 'no height information' might also be passed.
No further information need be given on the conflicting ac unless requested by the pilot or, in the opinion of the controller, the conflictor continues to pose a definite hazard.
In all of the deliberations on TI under RIS only pertinent information should be passed. Therefore, if another ac is definitely passing behind the subject ac and poses no hazard, unless it is likely to get reasonably close (5nm?) no TI is necessary.