You're assuming that Morgoth knew that the Eagles lived near Gondolin, and that he could associate the coming and going of the Eagles with the location of Gondolin. He didn't and he couldn't.
That the Crissaegrim was an abode of Eagles seems to have been little secret; Of Beleriand and it's Realms refers to it as such at a time before the building of Gondolin:
Upon the left hand of Sirion lay East Beleriand, at its widest a hundred leagues from Sirion to Gelion and the borders of Ossiriand; and first, between Sirion and Mindeb, lay the empty land of Dimbar under the peaks of the Crissaegrim, abode of eagles.
But there's absolutely no evidence to connect this with Morgoth's knowledge (or lack of knowledge) of the location of Gondolin, as is shown by Of the Ruin of Beleriand and the Fall of Fingolfin (with my emphasis):
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.
It wasn't in fact until after the release of Húrin that Morgoth got his first inkling of where Goldolin lay:
Yet there were ears that heard the words that Húrin spoke, and report of all came soon to the Dark Throne in the north; and Morgoth smiled, for he knew now clearly in what region Turgon dwelt, though because of the eagles no spy of his could yet come within sight of the land behind the Encircling Mountains. This was the first evil that the freedom of Húrin achieved.
This passage also confirms that the Eagles did a pretty good job of keeping Morgoth's spies out of the area. As Thorondor himself said:
If the Eagles of Manwe were wont to err thus, then long ago, lord, your hiding would have been in vain.
To re-emphasise, an earlier passage in Of the Return of the Noldor establishes that the main purpose of the Eagles was not to assist the Elves but rather to keep watch on Morgoth and bring news to Manwe:
For Manwe to whom all birds are dear, and to whom they bring news upon Taniquetil from Middle-earth, had sent forth the race of Eagles, commanding them to dwell in the crags of the North, and to keep watch upon Morgoth; for Manwe still had pity for the exiled Elves. And the Eagles brought news of much that passed in those days to the sad ears of Manwe.
And so there is no reason for Morgoth to even think that tracking the Eagles would give him the location of Gondolin.