This segment of the runaround takes you to the Dreyfoos side of the first floor of the Stata Center -- to the radar exhibit!
The radar dish (and its dishy core) are surrounded by a brief quotation from Professor Nelson Yuan-Sheng Kiang, arranged across three concentric arcs orbiting the large dish itself.
The puzzle presents a number of times paired with one of three depth indicators (Inner, Middle, or Outer). Imagining a clock face centered at the concentric middle of the three quotation arcs, the hour hand of these times would point to specific words within the quotation, while the depth indicator denotes which of the three quotation arcs to read from. Indexing into this word by the number of minutes then gives a letter.
For example, the "12:06 Middle" entry indicates that you should look at the word directly above the center of the dish and in the middle arc. That word is "RESEARCH", and its 6th letter is R.
Doing this for all the given times yields:
Heavens! It's the Signal Corps!