I read and asked a lot, before I finally figured it out. Here's how:
Dowload and install Bitcoin Core from the official download page -- https://bitcoin.org/en/download -- but DO NOT START THE PROGRAM in the usual way. Instead, open the Windows Command Prompt program and enter
cd\program files\bitcoin\daemon [return] .. then
bitcoind [return]
That starts the program, even though you see no indication of that in the window. You can't close the Command Prompt window or the program stops; but you can minimize it to the tray and it continues to run fine. After it's downloaded the blockchain and begun doing its regular function, you can check that it's running well this way:
Open a second Command Prompt window and enter
cd\program files\bitcoin\daemon [return] .. then
bitcoin-cli getinfo
If you've opened Port 8333, you should see more than 8 connections, and all is well with the world.
To stop running the node, you can just close the Command Prompt window it's running in.
1) Compile and build the client yourself without compiling in the wallet. Easy enough to do in *nix OS.
2) Start the service by passing the -disablewallet parameter.