 Yes, you need to take the movement all the way out. The pix is the speedo & tach from my '56 310, my '59 311b is the same so your '59 310b should be also. These are drag cup movements. The input cable spins a permanent magnet inside the drag cup. The hour drum is turned mechanically by the worm & spur gears. The seizure most often occurs in the input drive bushing. This is the best way I've found to free it up w/o breaking the drive loose from the magnet.
Fill the hose with PB blaster or similar penetrate and let it set until you can wiggle the drive loose. Be patient (sometime days or weeks), any force will destroy the movement. It is best to take the hour drum out, protect the face plate paint, and remove the wick from the oiler. Penetrate may soften the plastic in the drum and destroy the paint (you needn't ask how I know this). If you have time and are so inclined I would recommend that you do the speedometer first to get a feel of the process. Both movements are the same except sweep & input drive direction. The speedo sweep is the more common and easier to find a replacement. Good luck.
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