In todays market I would have thought you would be struggling to find a clean manual GT-T for $13k!
If you have the time I would suggest import, you can get pretty much the exact car you are chasing (be it kms, colour, auction grade, sunroof etc.) for a reasonable amount.
Kristian aka Iron Chef is great (he is a busy guy though and gets tonnes of emails every day, he can't always reply straight away), I can vouch for him having imported my Legnum through him, would have been a horrible, painful experience without an import broker. Ben over at J-Spec has some great feedback also so you will be in safe hands with him also.
If I was you (and I have previsouly bought an R34 already imported from a dealer) I would set my budget a little higher ($16k - $18k maybe?) and import the Skyline of your dreams.