male, the ICAO rulers for what you appear to have are set out in PANS-ATM (para 8.1.1). It says
8.10.1.1 When authorized by and subject to conditions prescribed by the appropriate ATS authority, surveillance radar may be used in the provision of aerodrome control service to perform the following functions:
a) radar monitoring of aircraft on final approach;
b) radar monitoring of other aircraft in the vicinity of the aerodrome;
c) establishing radar separation between succeeding departing aircraft; and
d) providing navigation assistance to VFR flights.
8.10.1.2 Special VFR flights shall not be radar vectored unless special circumstances, such as emergencies, dictate otherwise.
8.10.1.3 Caution shall be exercised when radar vectoring VFR flights so as to ensure that the aircraft concerned does not inadvertently enter instrument meteorological conditions.
8.10.1.4 In prescribing conditions and procedures for the use of radar in the provision of aerodrome control service, the appropriate ATS authority shall ensure that the availability and use of radar information will not be detrimental to visual observation of aerodrome traffic.
Note.— Control of aerodrome traffic is in the main based on visual observation of the manoeuvring area and the vicinity of the aerodrome by the aerodrome controller.
The document defines Radar monitoring as the use of radar for the purpose of providing aircraft with information and advice relative to significant
deviations from nominal flight path, including deviations from the terms of their air traffic control clearances.
If your authority has not set any specific instructions I would suggest that the radar is there simply to augment your view out of the window. If you know which aircraft is which from the SSR codes then you can provide useful navigation and flight information to pilots but this doesn't necessarily require you to tell the pilots that they're identified. I used to to the phrase "Traffic believed to be you ...".
If the target disappears I can't see any reason why you can't ask a pilot to reset the tx'der without being committed to providing a radar service. As an aside, in many circumstances in a radar environment I used to identify an aircraft but, quite specifically, not provide a radar control service - it's often very helpful to know that a target is a particular aircraft without having to take responsibility for any part of the flight if it isn't necessary.
The ICAO rules talk about vectoring traffic but I think if you look at other parts of the rulebook you'll find that this would only be possible if the aerodrome controller also holds a radar qualification or training specified by your authority. I'm afraid I don't really have time to dig out the references right now.
I hope this helps.