Engine light still stays on

The check engine light comes only when the computer control unit (called the PCM) senses a fault in the electronic controls of the engine and/or the emission system, there are about 200 possible faults that turn the light on, to know what has developed a problem you must have the system tested, this is called an OBD2 fault code test, Kragen and Autozone parts stores do this testing for free. Until the fault that turned the light on is correctred the klight will remain on, u can disconnect the battery for 5 minutes to clear the light or ask the parts store to clear it for you, as far as the reverse light problem goes u most likely have a defective reverse light switch, replace it.