Amp neon lights wont turn off

There are two types of power that feed your amplifier. There is a constant power that connects directly to the battery and there's a remote power that usually connects to the remote power output of your deck. Some decks do not have the remote power output, but they have a power antenna output that works just as well.
The remote power is what enables the amplifier to turn off when the car's power turns off.
Either way, it sounds like you have the remote power input on the amp connected to your constant power source.
That would prevent the light from turning off with the car.
If you don't have a remote power or power antenna output on your deck, I would invest in a new one.
However, it is relatively easy to find a remote and a constant power source in your fuse box.
Purchase a fuse tap for a few cents and connect the remote power input on the amp to a power source in the fuse box that turns on and off with the ignition.
Some of the power sources you can find in your fuse box that go on and off with the ignition may be labeled something similar to the following:
ignition, power windows, radio, accessory, etc.
The constant power sources in your fuse box are the ones that don't power off with the car, such as the dome/interior light, power locks, battery, etc.
I hope that some of this helps out a little.