I just saw your post. I have had 'caudal injections'. They are steroid injections into the caudal area which Did help w/ my coccyx/tailbone pain. But....the anesthesia was not general. General is when they completely knock you out. I w/b very surprised if they would do that for an injection.
Yes, I had the 'in the hand' thing. That is for light sedation and in case they need to get you hooked up to any other fluids/meds.
My first caudal was painful mainly bcuz the inflammation was very severe - had been building up for 3+ years. The second was easier and the combo helped me w/ that pain Tremendously!
Hope this helps a little.