Ultralights are regulated under 14 CFR 103 and there are very few regulations of any kind that apply to them.
The only specific lighting requirement is in 103.11(b):
§103.11 Daylight operations.
(a) No person may operate an ultralight vehicle except between the
hours of sunrise and sunset.
(b) Notwithstanding paragraph (a) of this section, ultralight vehicles
may be operated during the twilight periods 30 minutes before official
sunrise and 30 minutes after official sunset or, in Alaska, during the
period of civil twilight as defined in the Air Almanac, if:
(1) The vehicle is equipped with an operating anticollision light
visible for at least 3 statute miles; and
(2) All operations are conducted in uncontrolled airspace.
This question and this one have some information about what an anticollision light actually is (a beacon and/or strobe), but since ultralights are so lightly regulated I'd be surprised if anyone cares much about the exact form of lighting. However, you could check with your local EAA chapter or ultralight club to see what people typically use.