No it is not national trust. It will be either council owned or dept of environment ancient monuments section (or whatever their current name is). It is a bit sloping and may have occasional romantics parking at night but can’t see a problem otherwise.
Don’t forget the car park in Dundrum seems to be used as well. Height barriers are never closed, but perhaps noisy being beside the main road. Likely to be blocked in on Sunday mornings with the car boot sale nearby, but very handy for the Bucks Head or Mourne seafoods. The chip shop has a good reputation as well. All easily walked from the Castle car park as well, although a bit steep uphill last thing of an evening.
It is Dept of Communities but you will likely see signs for NI Environment Agency or even Dept of Environment. Responsibility for built heritage moved between depts a couple of years ago when the number of Depts in NI was reduced and some elements transferred to other Depts. It’s not council or National Trust anyway.
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