Does the organization of the kingdom under David and Solomon indicate a solar calendar was used at that time?

Question

Solomon divided his kingdom into 12 areas and had 12 individuals overseeing those areas. Then he had each area provide food for him for a month:

Solomon had twelve officers over all Israel, who provided food for the king and his household. Each man had to make provision for one month in the year. (1 Kings 4:7) [ESV]

The solar calendar has 12-months. A lunar calendar requires intercalating a 13^th every 2-3 years.

David had a similar division:

This is the number of the people of Israel, the heads of fathers' houses, the commanders of thousands and hundreds, and their officers who served the king in all matters concerning the divisions that came and went, month after month throughout the year, each division numbering 24,000 (1 Chronicles 27:1)

Chronicles continues by naming which person was responsible for the first month, the second month, and so on. As with Solomon's provisioning, there are 12-leaders for 12-months.

Do these organizations indicate they were following a solar calendar, at least for civil matters?

Answer 1

Not strictly, no. The ancient Hebrew calendar was a luni-solar calendar based upon the sighting of the new moon for the months, and would play catch up to the solar with an intercalary month of "ve-adar", or Adar Bet which would add a second Adar at the end of the twelve month lunar period every 2nd or 3rd year. It is actually still a very accurate calendar cycle, as is explained here. So, most probably, the second Adar would just fall in with the 12th officer David had set over the 1st Adar in the intercalary or "leap" year.