But perhaps it is possible that
Morgoth hinted at the possibility that there was an
Elvish realm 'there', since the
Eagles of
Manwë kept such vigil?
He was desperately looking for
Gondolin, and nowhere else in
Middle-Earth did the Eagles keep such steady watch, so perhaps Morgoth could have put 'one and one' together and figured it out? Though it probaly wasn't such an obvious or simple equation at all.
And no where else in Middle-earth did eagles abode. Morgoth would know that Eagles have the special favour of
Manwe and act as his messenger so they are bound to be hostile to him and his
creatures. Therefore, once he had found out Enciricling
mountains as Eagle's abode, he would have deemed their hostile behaviour and ceaseless watch as an
item to protect their eyeries and as an act of hostility they bore towards Morgoth.
Which one's and one's? It was popular belief, or was bound to be a popular belief, that
Turgon had developed his hidden Kingdom away in the south--In some forest or far off mountains. Morgoth didn't even knew the general direction of Gondolin till the
Hurin facade. He didn't have a lot of clues...did he...he knew Turgon had disappeared. Did he knew the name of Gondolin before Nirnaeth? No.
Rumour came to Morgoth of these things, and he was unquiet amid his victories; and he desired greatly to learn tidings of
Felagund and Turgon.
For they had vanished out of knowledge, and yet were not dead; and he feared what they might yet accomplish against him. Of Nargothrond he knew indeed the name, but neither its place nor its strength; and of Gondolin he knew nothing, and the thought of Turgon troubled him the more..
Gondolin was totally hidden from him till Nirnaeth except for the subtle disappearence of Hurin and Huor from which he learned that they had the friendship of the King of Gondolin.
No one, not even the
Noldor knew about where Turgon and his folks had went,
Then Ulmo returned to the sea, and Turgon sent forth all his people, even to a third part of the Noldor of Fingolfin's following, and a yet greater host of the Sindar; and they passed away, company by company, secretly, under the shadows of Ered Wethrin, and they came unseen to Gondolin, and none knew whither they had gone. And last of all Turgon arose, and went with his household silently through the hills, and passed the gates in the mountains, and they were shut behind him.
Through many long years none passed inward thereafter, save Húrin and Huor only; and the host of Turgon came never forth again until the Year of Lamentation after three hundred and fifty years and more.
Aredhel didn't even reveal to her Husband, Eol, the location of Gondolin.
As you yourself say it wasn't an obvious and simple equation. Probably no on except Ulmo knew about the hidden vale of Tumladen and besides no one would have thought that Turgon would build a secret refuge so close to
Angband.
But offcourse once the general direction of Gondolin was revealed, the equation would have become easier and he would have put two and two togather and found out the real purpose of the eagle's vigilance.
Also: How many entrances into Gondolin were there?
The dry river bed. The secret refuge that Idril built and through air.