Install your mandrel WITHOUT a pen blank on it. Including positioning the tailstock to hold it, as you normally would.
Turn the lathe on, is the center of your mandrel turning true? Or, can you see it "wobbling"? Most likely it wobbles. Put your toolrest in position and slowly touch the mandrel with a sharpie, coming over the toolrest. JUST TOUCH> turn off the lathe, you will have a mark on your mandrel. Tap it with a hammer (rubber mallet) ON the mark. You are bending the mandrel, back to straight. Continue this until you no longer get a MARK on your mandrel - instead you are making a RING around the mandrel. When that happens, you are straight.
TURN A PEN and GASP!! See, you're a mechanic, you just didn't know it.