The Brotherhood of Steel is aware that there's a bunch of good technology lying around in the Burham Springs mines. They want to prevent it from being distributed throughout the wastes by Phil, Sparky, and Frank. The core BoS does not want anything done to those three, but they do want to reclaim as much of the old tech as they can. However, the Circle of Steel has different plans. Even if you recover all tech from BoS, the CoS wants Phil, Sparky, and Frank dead. They also want to see the mines blown up via the placement of charges at specific locations in the mines.
Combat Boy, Stealth Boy - This is a fairly straightforward quest. The PC simply has to kill Phil, Sparky, and Frank, then set two charges at the entrance to the mines (next to two clearly marked supports). Destroying the supports causes the cave complex to collapse. If the PC is inside, it's game over. Otherwise, the screen shakes and a huge cloud of smoke emerges from the mine. After the smoke clears, there's only rubble in the entrance (any quest items inside are at the edge of the rubble).
Diplomacy Boy, Science Boy - There is no completion path specifically for these character types.
Traci Niels indicated that she wanted Burham Springs taken care of. And by taken care of, she meant that its three squatter residents should be killed and the mines should be destroyed by taking out the supports at the mineshaft entrance.
The Burham Springs Mines are now officially out of business. I destroyed the supports and a rockslide sealed the tunnel.
Traci was satisfied at the news of Burham Spring's collapse and zero population. She gave me a few items and thanked me for protecting the Circle of Steel.