not sure if you mean exterior lights or interior lights, but i'm going to assume headlights. check the grounds from each headlight going to the radiator support, they are probably loose or corroded
You must be in the rust belt- Terminals and lugs all need to be hosed off, The cable with a little red wire, with it's "lollipop" needs to be clean, the negative cable which goes to the chassis/ground needs to be cleaned at the bolt that holds them to the chassis, and the cable leading from the chassis ground to the engine block....also the age of the battery as these will be less willing to accept a charge 10% per year, so if it's gettin' old...it's gettin' replaced.
Which lights are flashing? The headlights should have a circuit breaker that could be popping. Do you have standard wattage headlights?
Looking for a Used Neon in your area?
CarGurus has 665 nationwide Neon listings starting at $1,500.
Search Dodge Neon Questions
Dodge Neon Experts
Related Models For Sale