The reverse light switch (sensor) should read 0 ohms or close to it when it is closed to indicate the machine is in reverse. The lights brightening as you rev up the motor is normal as the voltage rises as the motor revs faster . Check the voltage at the battery when the motor is running It should be about 12.5 at idle and rising to a maximum of between 13.5 and 14.2v . If it is low it could also be the source of the rough running , although the rough running, bogging and backfire is usually from the motor running lean. It could be from a missed plugged passage or just the idle air mixture out of adjustment. Check for leakage of the high tension wire to the spark plug and try a new plug too as the spark plug could be intermittent .