As for the end of its time, the majority hold that it extends until the sun passes its zenith. (1) Allah knows best.
The Second Issue: Neither a Call to Prayer nor an Announcement That Prayer Is Commencing Is Prescribed for the Two Eid Prayers
Neither a call to prayer, an announcement that prayer is commencing, nor the proclamation “Gather for prayer” is prescribed for the Eid prayer.
The evidence for this is as follows:
Ibn Jurayj narrated from Atā, from Ibn Abbās and Jābir ibn Abd Allah al-Ansārī, that they said, “No call to prayer was given on the day of Eid al-Fitr or Eid al-Adhā.” I asked him about this again sometime later, and he informed me, saying, “Jābir ibn Abd Allah al-Ansārī informed me that there was no call to prayer for the prayer on the day of Eid al-Fitr when the imam came out, nor after he came out. There was no announcement that prayer was commencing, no summons, and nothing whatsoever; there was neither a summons that day nor an announcement that prayer was commencing.” Reported by al-Bukhārī and Muslim. (2)
Jābir ibn Samurah said, “I performed the two Eid prayers with the Messenger of Allah—peace and blessings be upon him—many times, not merely once or twice, without a call to prayer or an announcement that prayer was commencing.” Reported by Muslim. (3)