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Well I would definitely start with Moebius 9010 (for train wheels and balance endstones) and 9020 (for train wheels) if you are working on Pocket Watches. Moebius 9415 is a must for Pallet/Escape wheel teeth. A quality silicon grease. Moebius D5 is essential (barrel arbor, motion work). Molycote DX or Moebius 9501 grease for keyless work. Moebius 9501 or 9504 for high friction (e.g. Cannon pinion, Setting lever spring and anything at high friction). Moebius 8200 grease for mainspring. Moebius 8217 for barrel wall (automatic watches) It's a lot but at a minimum get 9010, 9415, D5 and 8200 I hope this helps. Recommended Lubricants for Getting Started.pdf Moebius_Oil_Chart.pdf

If you shake it side to side does the balance swing freely? If so then autowinds advice is sound. But before removing the auto works will have to come off - this will be secured by two black screws. When lifing the auto work put a little pressure on the winder by turning it slightly then prise carefully using a screwdriver. Then taking out the balance is safer. Proceed then as per autowinds advice to see if the pallets are free. If the balance does not swing freely then it could be the balance tack. This is a small lever which moves out to touch the balance wheel (stopping it) when you pull the crown to the hand setting position.