At least a contact, once on TCAS, tends to stay on TCAS.
Exactly right. Let me emphasise the 'a' .
Especially in the example given above, all that you know is that you've got some target on your TCAS. In Jerricho's example, that's not worth a thing. It could be anything, it could be totally different from the target Jerricho is trying to point out.
Jerricho, keep scratching your head. If the reply is 'we can't see him but he's on TCAS' I would advise you to ignore the last part. They can't see him. Period.