The hail "hold your course" is not binding on a right-of-way boat. I still say it though. When I hail "Starboard", or "Leeward", I am simply alerting another boat that I'm there. When I reply to a hail with "hold your course", I only mean that I'm aware of them, and that I intend to keep clear. If you want, you can hail "I'm going to cross" or "I'm going to duck" instead. That would make your intention even clearer.
Hailing is not explicitly recognized nor required outside of rules 20 and 61. According to Dick Rose, however, rule 14 "AVOIDING CONTACT" implicitly requires hails, as they are a reasonably possible way to help avoid a collision. Many other judges disagree with that opinion though. Either way, I believe that they are still a good idea. "When Boats Meet" is much safer if they are aware of each other and know what actions to expect.
In a starboard/port encounter, although boat S has right-of-way, she still has an obligation to avoid contact under Rule 14. At some point, if P does not keep clear, then S has to take some sort of "avoiding action" (which is typically to change course or speed). S doesn't get carte blanche on when to make that decision. She must have a genuine and reasonable apprehension of contact. Take a look at ISAF Case 50 at
http://www.sailing.org/tools/documents/CaseBook20092012with2011changes-[9701].pdf which states:
When, after considering all the evidence, a protest committee finds that S did not change course or that there was not a genuine and reasonable apprehension of collision on her part, it should dismiss her protest. When, however, it is satisfied that S did change course, that there was reasonable doubt that P could have crossed ahead, and that S was justified in taking avoiding action by bearing away, then P should be disqualified.
Oh, and there is no specific rule regarding "tack or cross". It's just a common tactic in close port/starboard crossings.
I hope that helps,
Eric