Servos
Yeah, the strongest RC servos you can get that put out a maximum of about 10kg-cm/25lbs-in of torque. Titanium gears and stuff, about $115. The strongest RC servos I have seen by a very large margin.
https://www.hitecrcd.com/Servos/hs5995TG.htm
Of course, you can find cheaper more conventional servos around the range you specified. I am just show you the strongest, most durable, highest end one. BUT get a servo with metal gears for your application...trust me...you got inertial forces and vibrration of the light when moving the motor cycle around that the motor will have to fight. Be aware of the increased current requirement for digital servos over analog (conventional) servos. Its 5A@7.2V for the servo mentioned above. Also be aware of the 7.2V maximum found in RC servos which will require you to step-down the 12V motor cycle batteries to 6V-7.2V (for the servo sizes you need) with a capacity of ~5A per servo motor used (for the servo mentioned above, current draw will vary from servo to servo).
Do you need move 5-10lbs or do you need 5-10 lbs of torque? There is a big difference when the lever-arm mechanics kick in.
RC servos use a PWM input pulse that they process to determine the position to move to. When powered off, they STAY WHERE THEY ARE. Some fancy radio receiver systems for use in model airplanes might reset the servos to certain positions during a power failure using stored capacitor power...but they aren't something built into the servo.
When I spoke of the gyro-servo not being able to properly compensate if the gyro detects motion beyond the servo's range of motion, I hope you understand what I am talking about. But now that I think about it, the gyro may make the servo move in the opposite direction at the opposite speed it is detecting (rather than making the servo move the opposite distance that the gyro is detecting, since this would mean the gyro processor has to do some nasty inaccurate math with the raw angular velocity output that gyros output). This would mean that the gyro may not be able to compensate if the motor cycle tilts too fast, but you should never exceed that speed either. So basically, you probably dont need to worry about either of these problems- your motor cycle should never EVER tilt far enough or fast enough for the gyro to not be able to compensate. If you do have to worry about these problems...you got much more serious problems on your hands, God forbid.
I kind of don't understand why a motor cycle light blinds someone...is it because the light is made to face at the ground and when tilting it points up?