Anneelaine, you could be on to something here and may have solved it yourself. Like any research you do need positive proof and it has been difficult to get that.
However, if I could just explain this first so you can be aware of what has happened already:-
From the Black Cat area to Llandudno Junction (over the Railway Bridge) was called the Monk's Causeway and the area in Llandudno Junction is known as Pensarn
In English Pensarn is the top or head of the causeway. I've found Pensarn Farm on the Llandudno Junction side and we know that it was in the Parish of Llangystennin however today I've looked at a map of the 1880's and it also shows a Pensarn Farm on the Black Cat side of the causeway and this could be the one you are seeking.
Was that farm in Llangystennin Parish? At present I'm not positive but perhaps someone on here can tell us one way or
another.
Anyway, I've been to have a look in that area and the first building on the right going up the hill is a very old building, it has other smaller buildings in the yard but is completely private and shielded from the public view. There is no name on the building, no front door, just a large wooden gate and protected by one or two noisy guard dogs so I kept well away.
I've taken some photos for you but there may be other forum members who may be able to put some name or history to the place. Further up the hill is a large white house called Castle Keep and next too it on the main road is another property with a number of stone steps going up to it.
I've just had a look at the postcode you have supplied LL28 5LE and there are just 3 properties coming up for that and they are Castle Keep, Maes Glas and Sarn Y Mynach . I'm thinking that the house on the corner with the ivy on it is called Sarn Y Mynach but that's just my guess.