To get to the root of the cause, you may have to disassemble . But before you do that, I gather this is a replacement sweep hand? What is the movement make and caliber and are you sure this is the correct size sweep hand for the movement. If the watch is running steadily while the sweep hand stutters and there is no tension spring, then the seep second pipe is either the wrong size, or it was squeezed onto the pivot....can you provide more info?
Well, I tried the heated needle trick for an hour or so, but maybe got through 4 minutes of crystal edge removal. If I had 2 full work days to do it, and wasn't occasionally skipping out of the groove and scratching the rhodium, I'd have continued with that. There was no getting it to spin towards removal, as it was well glued down. However, with the movement not cooperating with its resurrection, and the eons it might take to remove what was left behind of glue and plastic, I decided to go the nuclear option.
What I couldn't tell, is how the rhodium reflector was held in. There was a very small space at the bottom that a razorblade might have fit it. However, with the way things (needles and screwdrivers) were scratching that rhodium, I decided that this too was a bad idea. So I broke out the acetone.
I knew that acetone worked well with the plastic beads used for preserving fossils, FWIW. I figured that it would eventually break down the acrylic crystal and glue, so I gave it a long soak. Unfortunately, there were some stripes that were painted on. They added to the interesting look of the watch, so I was sorry to lose them. They had looked like they were actually recesses formed in the rhodium. That's what fooled me.
Well, after that long soak, both the rhodium reflector and what was left of the crystal and glue came out nicely. I'm not happy about losing those white lines, but it really was ridiculous to have to melt the plastic away a millimeter at a time as each needle becomes a little softer with heat.
If I had it to do over again, I would probably try to get a razor blade or Exacto under the reflector to see if it would pop out. That way the white lines would be intact. Another thing one might attempt is using a heat-gun on the case, getting it very hot, but not glowing, and seeing if it softens the glue and plastic enough to get it out. Bear in mind that case will be very hot, so use something to insulate yourself from burn pain.
This particular Wittnauer case number is #6519. So if you ever get to do a crystal replace on it, you might consider using the X-acto. Just be careful, as it could easily slip and scratch the rhodium and/or slice your body part. Cheers.
I found some additional information you might find useful.
Then on page 7 of the PDF it talks about the application.
BHI The Practical Lubrication of Clocks and Watches Version 2008.0.pdf