Dear OLG
As far as ICAO rules are concerned, I would answer your question as follows.
If you fly maintaining own separation the blanket clause of ICAO Annex 2, Chapter 3, sec. 3.2.1 applies, which, of course, applies to all flights, controlled or not:
3.2.1 An aircraft shall not be operated in such proximity to other aircraft as to create a collision hazard.
In my opinion there is no ICAO provision that states a specific horizontal separation for the case you asked for. As for vertical separation, you are compelled to maintain the appropriate cruising levels (ICAO Annex 2, Chapter 5, sec. 5.2.2 and 5.3.1).
Concerning TCAS (respectively ACAS in ICAO terminology) there is no ICAO provision that obliges a pilot to follow a RA. There are, however, the provisions for the right-of-way in ICAO Annex 2, Chapter 5, sec. 5.2.2, but the PIC
may depart from these rules in circumstances that render such departure absolutely necessary in the interests of safety (ICAO Annex 2, Chapter 5, sec. 2.3.1).
Needless to say, a RA would be one of these circumstances. ICAO Annex 2, Chapter 3, sec. 3.2.2 clarifies this:
The aircraft that has the right-of-way shall maintain its heading and speed, but nothing in these rules shall relieve the pilot-in-command of an aircraft from the responsibility of taking such action, including collision avoidance manoeuvres based on resolution advisories provided by ACAS equipment, as will best avert collision (ICAO Annex 2, Chapter 3, sec. 3.2.2).
Note that this provision speaks of a 'responsibility'. If the PIC was obliged to follow a RA it would say 'the pilot-in-command shall'.
I hope this will point you in the right direction.
Take care
hvogt