I hope you meant red LED accent lights instead of neons. Neons draw a LOT more than LEDs.
Hopefullt you have a voltmeter on so you can monitor the draw if they are neons.
Case in point, a simple neon license plate frame will drain a battery, my led accents lights (6 8 light bars placed on the bike) however can be left on 4-5 hours while it is twinkling away in a bike show
Patriot Guard Rider
2000 VN750 Sere (Serendipity)
1990 GL1500 (Ole Blue)
1986 VN750 EVie (project bike, heavy custom)
VROC # 11628 / 25000-H
ARVROC # 12 Coordinator and Crowd Control
OKVROC # 18 (H)
TNVROC # 45 (H)