Question: Genesis
1:14 declares that the heavenly "lights" are to determine the
appointed times.  Doesn’t this disprove
the Dawn after Conjunction method for reckoning New Moon Day?

And Elohim said, Let there be lights
in the firmament of the heaven to divide the day from the night; and let them
be for signs, and for seasons [appointed times], and for days, and years:  (See Genesis 1:14.)

Answer: "Lights"
here is referring to the celestial bodies themselves, not necessarily to the
light that they emit.

And Elohim said, Let there be lights
<Strong’s H3974> in the firmament of the heaven to divide the day from
the night; and let them be for signs, and for seasons [appointed times], and
for days, and years:  (See Genesis 1:14.)

H3974 (mâ’ôr/me’ôrâh)
– "From H215; properly a luminous body or luminary, that is,
(abstractly) light (as an element); figuratively brightness, that is,
cheerfulness; specifically a chandelier: – bright, light." (Strong’s Greek & Hebrew Dictionary)

The Hebrew word used in Genesis to denote visible light is <H215> and <H216>. 
For example

And Elohim said, Let there be light <H216>: and there
was light <H216>. And Elohim saw the light <H216>, that it was
good: and Elohim divided the light <H216> from the darkness.  (See Genesis 1:3-4)

And Elohim set them in the firmament of the heaven to give
light <H215> upon the earth, And to rule over the day and over the night,
and to divide the light <H216> from the darkness: and Elohim saw that it
was good.  (See Genesis 1:17-18.)

Genesis 1:14 in no way disproves the Dawn
after Conjunction method of reckoning New Moon Day, for this method is in every way
dependent upon Yahuwah’s appointed luminaries (H3974).