I figured out an inexpensive shortcut with parts you can get from the local Lowe's / Home Depot / Menard's / etc.
In addition to all the regular tools, you will need:
- 1/8" x 1-1/2" (or longer) brass pipe nipple
- 4 feet of clear plastic tubing that will fit over the end of the pipe nipple
- a battery-operated inflation pump that also has a suction port (I used a Coleman # 2000000834)
After draining the old coolant and removing the radiator top plug, carefully thread the pipe nipple with attached tubing into the hole. It doesn't have to be very tight - just a turn or two to hold it in place should suffice. Fill the coolant expansion tank over the engine with appropriate coolant. While holding the pump above the height of the coolant expansion tank, turn the pump on. It will draw air out of the system and the coolant level in the expansion tank will fall. Try to keep at least some coolant in the expansion tank at all times - you don't want to draw any more air into the system. It might be useful to have a friend assist with this step. Repeat until pure coolant (not mostly air with coolant spraying around in it) appears in the tube between the pipe nipple and the pump. Do not let the fluid level in the tube reach the pump. At that point, bend the tube over itself to seal it and disconnect the pump. Now, pull the tubing off the pipe nipple and in the same motion, put your finger over the end of the pipe nipple (if you don't do this you'll have a gusher and you'll probably need to start over). Now, rapidly remove the pipe nipple and re-install the radiator plug. I wrap the plug with Teflon plumbing tape before re-installing to make it easier to remove in the future.
At this point you will probably find that the system is mostly filled, and that coolant will circulate in the system and the radiator will heat up. Proceed with the rest of the fill procedure as outlined in the Brammo manual.
Important Note: The reason for keeping the pump above the height of the coolant expansion tank is so that coolant doesn't siphon into the pump. If coolant (or any other fluid) gets into the pump, it will likely be ruined.
