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1) To push the piston back so that the new (really thick) pad can be inserted, do you have to simultaneously turn the 4mm adjustment screw while putting pressure on the piston? On the driver side, I guess you would turn it CW since CCW moves the piston towards the disc (and it does move). When putting pressure on the piston without turning the screw, the piston didn't budge.
For the outer piston, yes, use some pressure to push it in while you attempt it. It could be that the internal adjuster mechanism inside the piston is rotating. For that you need a high speed wrench. Air wrenches are instant on and off. The velocity of an air wrench can make this move. For the inner piston, first, put a heavy glove on and move the arm back and forth. The piston is probably stuck a tad in the bore. This will break that bond.
Next, try the adjuster screw again. Yes, it is always good to apply some pressure but not always necessary.
Remember, the adjusters do nearly all of the work moving the pistons in and out. The outer one (the one you can see through the wheel acts like a normal screw. Turn it clockwise and you will pull the piston back into the caliper. The "inner" adjuster is the same except that it is gear driven so, that makes the entire operation work in reverse.
Again, move the handbrake arm first to see if you can break the piston free.
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Regarding the following pics of the inner adjuster:
2) How can you see the inner cap to tell if it's easily going to come off using the 4mm hex on the 6" socket extension (through the control arm)?
You should be able to look up from the bottom of the control arm to see it. Use your best judgement. You may want to get a drift to go through the hole in the arm first and smack the 10x1 gear cover. This can help break the bond that has. If you feel the 4mm hex starting to go, stop and remove it with the cold chisel. This way you can still use the cover until you purchase a proper 5mm one.
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3) Assuming I can get the inner cap off and out of the way, do you need to remove the inner washer and gear or just go ahead and stick the 4mm hex back in and turn?
Just go ahead and stick the 4mm in there and turn. You would do well to watch the washer and make sure it doesn't come off though.
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4) If it seems like the cap is stuck, should I follow the Pelican method of removing the rear caliper (without disconnecting the brake lines)?
Pelican Text:
***Simply remove the two bolts that hold the rear caliper onto the trailing arm and the clip that holds the connection point between the rubber brake lines and the steel brake lines. You then should have enough room to take the caliper and get a set of needle-nose vise-grips on the stripped cap.***
I would not do this. First of all, let's address brake lines and how they're mounted to the control arm:
1. Early arms have a complete tab with a hole in it large enough for the end of the brake cable to go through it. The method of removing the clip will simply not work here but, it's not spelled out in that article.
2. Late arms have a slot that leads to the same size hole. If you have later arms you can remove the clip and slide the hose outward until the thinner hard line can slip up through the slot.
3. If the 4mm hex didn't work, I'll almost guarantee that needle nose pliers will only laugh at you... even Vise-Grip models.
In for a penny, in for a pound at that point. Leave the hardline on the caliper and disconnect it where it meets the softline. Take it to the vise and have at it.
Good luck.