There are two approaches to understanding and accepting lunar time.
1. Being led by the Spirit and accepting it by faith is the easier way.
2. The harder, more complex method is the logical, reasoned process of studying and evaluating all the evidence and arriving at a conclusion.
In my own experience, I was first inspired and convicted with the belief while later (over three or four years time) I looked for the logical proof and did the difficult study.
I call these two ways "led by the Spirit" and "forcing the intellect" or "right brain" and "left brain" or "intuitive" and "logical". The first is easy and simple, the second is difficult and complex. Both will lead to the same conclusion if one is guided by the Spirit.
LED BY THE SPIRIT
Without any consideration or study at all, it is hard for the Spirit to start leading. The pump must first be primed. So I will share my path. You may find or prefer a different path. I recommend that you NOT click any links until AFTER you've given inspiration a chance to work. The links are for those who want all the details (I warn you, it is more difficult).
1. Ask yourself whether time and calendation (calendars) have always been the same.
2. Study new moon days in the Bible and question their purpose - why were they given and why are they omitted from most Bible teachings (were they given in the Bible by mistake? Were they rescinded? Do they not apply to me?).
3. Study Bible prophecies and especially consider the phrase "think to change times and laws".
4. After the Spirit has convicted, learn how easy it is to know when Sabbaths occur.
Questions for the Spirit
Our current calendar is the Roman Gregorian calendar. When was it devised? What was before it? The previous calendar was the Roman Julian calendar. When was it devised? What was before it?
What calendar did Jesus, the Messiah use? (assuming that if it was incorrect, he would have said, but didn't, so it must have been correct). see "Calendars in History"
I then went very far astray by assuming the Jews must have answers, so studied what they said and did. It would have been better to learn from the Words of the Master who said the priests and rabbis were sons of Satan [John 8:44]. It consumed about two years to learn about their apostasies and the Talmud, their "holy" book of lies and human reasoning (rationalizing). Don't look to any of these for truth or even for accurate history.
Most experts agree that ancient Israel used a luni-solar calendar. Most experts agree that the Israelites observed the moon to determine the start of the new month. Very few "experts" understand that a new month also started a new week. No week ever straddled a month boundary (incomplete weeks in each month). Every week was complete before a new month began. Yahweh leaves nothing incomplete or dangling. Very few experts understand that there was only one calendar that was used for ALL holy days - the yearly feast days AND the weekly holy days (Sabbaths).
2. New Moon Days?
This brings us to "new moon days". Study all Biblical references to new moon days (there are only a couple dozen). You will be convinced that these days exist, that they are mandatory and that they are not weekly Sabbaths, but neither are they work days. They are holy days - days in which the temple was open and no work performed. You will find that new moon days are frequently mentioned in the same breath or sentence as "Sabbaths" (new moon days and Sabbaths). see "New Moon Days"
Decide what you will do (under inspiration of the Spirit) with new moon days - accept them or discard them.
The beast (Satan's proxy power on Earth) will think to change TIMES AND LAWS [Daniel 7:25]. What time has been changed, if not the calendar? What laws could be affected if not the fourth law of the ten commandments?
Would it be surprising then, to find these changes? Should we look for them? When did they occur and who made the attempted changes? Some teach that the Sabbath was changed from Saturday to Sunday, but NEITHER of these days existed in Israel at the time of Christ. BOTH are fictional days that only appear on the Roman calendar, not in scripture. The actual change was from the 7th day of creation under the luni-solar calendar to Saturday and/or Sunday under the Roman calendar (Saturday AND Sunday are BOTH counterfeit days of worship).
Can I find any changes to time other than the calendar changes made by Rome, effecting the Sabbath or any other of God's laws? see "Think to Change Times and Laws"
4. Technical Instructions?
A new (empty or dark) moon is a new moon day and a rest day and signals the start of a new month and a new week. Seven days later (when the moon is half full) is Sabbath. Seven days later when the moon is full is Sabbath. Seven days later (when the moon is half full) is Sabbath. Seven days later (when the moon is dark) is Sabbath. The next day and possibly the day after, will be a new moon day. Repeat. This is Yahweh's calendar in the heavens, just as the rising and setting sun is His heavenly clock. see "Finding Yahweh's Sabbath"
Ask the Spirit if this rings true.
I have linked some concepts for further study and will some day re-write the long, tedious, intellectual study, but it us much easier and safer to accept this truth on faith. With additional time, study, and spiritual maturity that faith will grow into a certainty.