Sunray etc aren't callsigns as such, they're 'radio appointment titles' for the commanders/representatives of the various arms and services. Paraphrasing a very declassified source (bracketed bits are examples, not gospel) [square bracketed bits are my guess at the Americanese equivalents]. Useful ones are:
SUNRAY Commander (Bn/Coy/Pl)
SEAGULL G Staff(Adjutant/CSM) [S-1]
KESTREL Ops Staff [S-3]
MOLAR Q Staff (QM) [S-4]
ACORN Intelligence (IO) [S-2]
PRONTO Signals RSigs
SHELDRAKE Gunners RA
HOLDFAST Sappers RE
PLAYTIME Transport RCT
STARLIGHT Medics RAMC
RICKSHAW Ordnance RAOC(showing my age: RAOC + RCT = RLC nowadays)
BLUEBELL Maintenance/recovery REME
WATCHDOG Provost
FOXHOUND Infantry
IRONSIDE Armour
HAWKEYE Army helicopter support (mmm - says ACC but wonder if it should be AAC...)
FORTUNE Forward Air Controller (RAF liaison)
These are all very British and, given the S- system the Yanks have, are/were probably not a NATO standard.
Callsigns proper were number-number-alpha but prefixed with an alpha callsign identifier/indicator (?) so a full example might be K13C. This, I think, was pretty standard across NATO. Given the last alpha would normally relate to a single vehicle or a section, we have a handy hierarchy up to battalion level:
CI Coy/Sqn Pl/Tp Sec/Veh
K 1 3 C
Bn HQ units would probably be alpha-0-number-alpha, Coy HQ alpha-number-0-alpha.
I'm not going to bet my life on much of the above, but it might shake out someone who does know!
The fly in the ointment is that OFP has only got the alpha-colour identity; though BAS configured a lot of additional Group and GroupColour options...