low on oil
The year, make and model info would help.
would a bad battery cable in a 95 toyota corolla make a engine come on?
make sure your gas cap is on tight. sometimes this will make your check engine light come on.
you might hit a puddle or a big bump that shook the vehicle to make the light come on
You can make music come on with a light switch the same way you can make a light bulb come on - plug a radio into the switched outlet.
Check the brake fluid level in the reservoir there is a sensor there that will make the light come on if your level is low.
There are dozens of things that turn the light on. Get the codes read at the auto zone.
Check bulbs to make sure all are working
no oil
It would be one of the conditions that could cause this.
applying pressure to the brake pedal
Not directly, but it may make the light come on if there is high manifold pressure from the high backpressure. The check engine lights usually only apply for sensors and indicate a larger problem.