Electrical problem with a power wheels

You most likely miswired the switch into the line that powers the foot pedal.

You'll need to post detailed photos or an accurate wiring diagram in order for anyone to understand what the problem is. We need more information.

When in doubt, undo what you did and see if it returns to proper operation.

We need to know a lot more ?
How did you wire the lights ?
Where exacitly did you tie into the wiring system ?
How is the power wheels wired ?

Many Many possabilities !

For a lighting circuit of this kind you would wire the lights to the wires that go to the two battery terminals.

For this project you should not have had to disconnect any of the existing wires. If you did then you probably created the problem that way.

What kind of lamp did you use? Traditional automotive turn signal lamps (let alone headlight lamps) draw a lot of power and the Power Wheels may have a circuit breaker that tripped on you. Or maybe the power draw was enough to melt the soldered connections of too thin wires they might have used and something has now fallen apart.

I am guessing that a Power Wheels would need at least 16 gauge wiring for the motor circuits, possibly 14 gauge. The same wire sizes (14 gauge for 15 amps) apply to 12 volts as apply to 120 or 240 volts. (For long runs, you actually have to upsize for low voltage applications; that's a ong story that is not on topic here.)