If you think that $13k is all it is going to cost you, you are sadly mistaken.
There are many GTR's for sale that are very cheap but it is for a reason. With GTR's nothing is cheap and if you get one that has not been looked after you will find out how expensive they can be and if you are tracking it you will find out most likely on your first track day with it.
For now... There are many ways to make a car run well during a test even if its fkd. Running thick oil, cutting wiring to warning lights etc, etc. If it really is mechanically sweet it seems VERY cheap even despite average body and interior condition. Logically though, if it looks rough inside and out I dont think it would have been looked after very well which means if you buy it you will be the one paying for that neglect.
For a cheap track day car, an R32 GTR simply does not work cause they just arent cheap when including all costs.
As suggested by others above, an R32 GTS-T is a much better alternative and they are quite resiliant, besides which a replacement rb20 is pretty cheap anyway!