Society of Broadcast Engineers * Chapter 78 * Blue Ridge Area of Virginia
ADC makes a really good tool to insert and remove BNC connectors from those compact HD video patch panels.  Its ADC Model: BT2000-xx where "xx" is the length of the handle in inches (6, 12, or 24). They are available from Markertek (in stock) or Broadcaster's General Store for less than ($100).  We looked for months for a "removal" tool. It turns out it's called an "insertion", or, "insert/extract tool."