The Encyclical of Basiliscus was signed by a great number of Eastern bishops, over 700.
We have a record of a gathering of local bishops in Ephesus who signed it, and they take the opportunity of mentioning those councils they consider authoritative, and which includes Constantinople I. This would have been in 475AD. This quotation is from the Chronicle of Zachariah.
"But now that the light of the true faith has arisen upon us, and the dark cloud of error been rolled away from us, we make known by this declaration our true faith to your Majesties and to all the world. And we say that freely and with willing consent, by the aid of John the Evangelist as our teacher, we have signed this Encyclical; and we agree to it and to everything in it, without compulsion, or fear, or favour of man. And if at any future time violence shall meet us from man, we are prepared to despise fire and sword and banishment and the spoiling of our goods, and to treat all bodily suffering with contempt; so that we may adhere to the true faith. We have anathematised and we do anathematise the Tome of Leo and the decrees of Chalcedon ; which have been the cause of much blood-shedding, and confusion, and tumult, and trouble, and divisions, and strifes in all the world. For we are satisfied with the doctrine and faith of the apostles and of the holy fathers, the three hundred and eighteen bishops; to which also the illustrious Council of the one hundred and fifty in the Royal City, and the two other holy Synods at Ephesus adhered, and which they confirmed. And we join with them in anathematising Nestorius, and everyone who does not confess that the only-begotten Son of God was incarnate by the Holy Ghost, of the Virgin Mary; He becoming perfect man, while yet He remained, without change and the same, perfect God ; and that He was not incarnate from Heaven in semblance or phantasy. And we further anathematise all other heresies." But they wrote down some other things. And they applauded with loud voice and approved.
It is interesting that all of the latter councils which they accept are viewed as Nicene, and not as additional in their own right. It is the one Nicene Faith which is propounded by all four councils - Nicaea, Constantinople, Ephesus I, Ephesus II.