I've crossed the land border into northern Turkey a few times (on an EU passport). They check passports very thoroughly in both directions and a couple of US passport holders were taken off the bus on the way in, but I have no idea why. I spoke to several regular travellers on my last trip and they said that the Turks are very fussy about passports, whatever their origin. They are very concerned about fugitives, apparently.
Wouldn't it be worthwhile to contact the Turkish embassy where you live?
As I'm sure you know, TRNC is not recognised
de facto as a nation and many insurance companies will not cover you for travel there as part of their standard policy. It's well worth the visit though. Cyprus as it used to be - and not a Russian in sight!
It might also be worth checking with the Lonely Planet Thorn Tree site - I've always found it helpful and accurate:
Cyprus - Lonely Planet travel forum