What are the laws on going out at night in a kayak?

unless you have a super long one... 1 360 light dusk to dawn minimum

Long story short--considering the interplay between state and federal law, the mininum requirement is that from sunset to sunrise kayaks must display a white light that is visible for two miles.

Jump on amazon and snag a few rolls of leds. Put the white ones on a pole about 4 ft long so you have your legal lights. Green ones on the sides to attract fish. They work lik magic to pull the fish in.

This is off the TPWD website, there has been a lot of debate and discussion over this in the past.
Remember that sometimes there's legal and there's safe, best to be both, IMO.

Paddling at night: Remember that you must carry one bright white light that can be exhibited in time to prevent a collision. It is recommended that you carry a lantern, flashlight, or other attached white light that will be visible from 360 degrees. Regulations state that canoes, kayaks, and all other manually driven vessels shall exhibit sidelights and a sternlight, and shall exhibit at least one bright light, lantern, or flashlight from sunset to sunrise when not at dock.

I run one Visi Carbon Pro 360 light and I keep StreamlIght by Waypoint (very bright LED spotlight) within easy reach just in case a Power Boat is getting to close.

From the Texas Parks and Wildlife Code:

"Sec. 31.064. LIGHTS. A vessel or motorboat when not at dock must have and exhibit at least one bright light, lantern, or flashlight from sunset to sunrise in all weather. A vessel or motorboat when underway between sunset and sunrise in all weather must have and exhibit the lights prescribed by the commandant of the Coast Guard for boats of its class. No other lights that may be mistaken for those prescribed may be exhibited."

"Sec. 31.073. CANOES, PUNTS, ROWBOATS, SAILBOATS, RUBBER RAFTS, RACING SHELLS, ROWING SCULLS, KAYAKS, AND OTHER PADDLE CRAFT; EQUIPMENT EXEMPTIONS. (a) All canoes, kayaks, punts, rowboats, sailboats, rubber rafts, and other paddle craft when paddled, poled, oared, or windblown are exempt from all safety equipment requirements except each vessel must have the following:
(1) one Coast Guard approved wearable personal flotation device for each person aboard; and
(2) the lights prescribed by the commandant of the Coast Guard for vessels and required under Section 31.064.
(a-1) Notwithstanding Subsection (a), a vessel described by that subsection, except a canoe or kayak, that is 16 feet or more in length must be equipped with at least one Type IV personal flotation device of the sort prescribed by the regulations of the commandant of the Coast Guard.
(b) Racing shells, rowing sculls, and racing kayaks while participating in or practicing for an officially sanctioned race are exempt from all safety equipment requirements except the lights prescribed by the commandant of the Coast Guard for vessels and required under Section 31.064.
(c) In this section, "racing shell," "rowing scull," or "racing kayak" means a manually propelled boat:
(1) recognized by a national or international racing association for use in competitive racing;
(2) not designed or used to carry equipment serving any purpose other than competitive racing; and
(3) in which each occupant, except a coxswain, rows, sculls, or paddles."

And from Rule 25 of the Rules of Navigation:

"(ii) A vessel under oars may exhibit the lights prescribed in this rule for sailing vessels, but if she does not, she shall [exhibit an all around white light or] have ready at hand an electric torch or lighted lantern showing a white light which shall be exhibited in sufficient time to prevent collision.Vessel Under Oars"