The reign spoken of in Rev 19-20 is a rod of iron reign over the nations, not a general reign of Christ without definition as Amill is trying to present.
The rod of iron reign does end, when satan is released from prison.
Rev 2:25 But that which ye have already hold fast till I come.
Rev 2:26 And he that overcometh, and keepeth my works unto the end, to him will I give power over the nations:
Rev 2:27 And he shall rule them with a rod of iron; as the vessels of a potter shall they be broken to shivers: even as I received of my Father.
Rev 2:28 And I will give him the morning star.
Rev 2:29 He that hath an ear, let him hear what the Spirit saith unto the churches.
Rev_12:5 And she brought forth a man child, who was to rule all nations with a rod of iron: and her child was caught up unto God, and to his throne.
Rev 19:15 And out of his mouth goeth a sharp sword, that with it he should smite the nations: and he shall rule them with a rod of iron: and he treadeth the winepress of the fierceness and wrath of Almighty God.
Rev 19:16 And he hath on his vesture and on his thigh a name written, KING OF KINGS, AND LORD OF LORDS.
Rev 19:17 And I saw an angel standing in the sun; and he cried with a loud voice, saying to all the fowls that fly in the midst of heaven, Come and gather yourselves together unto the supper of the great God;
Rev 19:18 That ye may eat the flesh of kings, and the flesh of captains, and the flesh of mighty men, and the flesh of horses, and of them that sit on them, and the flesh of all men, both free and bond, both small and great.
Rev 19:19 And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against him that sat on the horse, and against his army.
Rev 19:20 And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
Rev 19:21 And the remnant were slain with the sword of him that sat upon the horse, which sword proceeded out of his mouth: and all the fowls were filled with their flesh.
Rev 20:1 And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand.
Rev 20:2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years,
Rev 20:3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.
Rev 20:4 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
Rev 20:5 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection.
Rev 20:6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.