Hmm, sounds a bit funny, you finding only 7 volt sources hollowch. Since this is a 12 volt system, almost every circuit you check should have almost exactly what your battery has.
You've got a wiring issue somewhere important. The only 7 volt circuit you should be able to find under the dash is the ignition resistor wire. The instrument cluster IVR runs on less, but it's a pulsing voltage signal, so you couldn't use it for anything normal anyway.
You have what's known as a "voltage drop" somewhere. That's resistance to flow, such as you'd get with rusty or loose connections, old corroded wires, bad battery cables, bad grounds due to rusty metal and stuff like that.
To keep from having to always be chasing electrical gremlins, I would trace back along your main power feeds first, to see what's up.
What year is yours again? Can't remember if that was you, but in the last couple of days someone was trying to clean up a super rusty fuse block in a '68. Something like that could cause low voltage readings in multiple circuits. Might check there too.
Paul