Does a new moon indicate the 1st day of the month?

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Lunar Sabbatharians refer to this as the bible calendar. "From one New Moon to another and from one Sabbath to another, all mankind will come and bow down before me," says the LORD. Isaiah 66:23. This was one of the verses Pastor Gideon used in the Sabbath study (lesson 12) which I think triggered the questions around using the moon to measure time and the significance of New Moon. Yes the new moon is the 1st day of the Hebrew month (1 Sam. 20:24-27), but this does not mean the weekly cycle or the Sabbath is governed by it. Concerning ‘new moon,’ in Isa. 66:23, standard lexicons agree that in connection with the special grammatical construction of this verse, the preferred translation is ‘month,’ thus rendering it ‘from month to month.’ Ninety percent of the time the Hebrew word is translated as ‘month,’ and 10% as ‘new moon.’ The Geneva Bible, Young’s Literal Translation, New English Bible, the Septuagint, etc., correctly translate this phrase as ‘month to month’ – which links up well with Rev. 22:2 (the tree of life that yields fruit every month). So once again, this passage does not mean that the moon will determine time in heaven.