when you power up the UNO the servo will find the "center" and stay there
Without extra hardware, that is never going to happen.Hint: it isn't a servo anymore, despite what the seller tells you.I think, under UK law, you'd have a very strong case for a refund.
So what you are saying is that I have the wrong type of "servo" for what I want to accomplish?
is this what you want to see?
the line i made runs perpendicular with the white plastic arm
It's a continuous rotation servo. There is no center point. There is no 0 degree mark, either. All such capabilities have been removed from that servo, to make it a continuous rotation servo. All that you can do with that "servo" is change the speed and direction that it rotates.
It's a bidirectional variable speed geared motor drive that is controlled by a pwm pulse.
"If this were a servo motor, it would take a set point and adjust its position to be at the corresponding location, using internal feedback. If this is a continuous rotation motor, it takes a set point and scales its speed depending on that set point, but there's no closed loop control, so it's not a "servo". This device may very well be in a package typical of servos and may even have been a servo before someone broke the feedback loop, but it's not a servo if it's continuous rotation, open-loop control."