The last couple parts arrived for the vacuum system allowing me to wrap up the wiring. I sketched up a schematic to help me get the wiring right.

Here it is all wired up.

Upon the first test, the vacuum pump only ran for about a half second and then stopped. I thought the vacuum switch may have failed, but it turns out it only needed adjusted. Apparently the factory setting is such that only the slightest vacuum will open the switch, and the hysteresis of the switch was sufficiently high that venting that tiny bit of vacuum wasn't enough to reset the switch to it's normally closed state. I made the adjustment, and now the vacuum system holds between 24 and 25 in Hg.