could be a high resistance joint at that connector. On mine the Positive lead of the starter is also where the wire that goes to the fuse links (and rest of the power supply for most everything else) is tapped. Since you are getting low voltages at the cars voltmeter and I presume at the fuse block (inside the car), I would start with just making up some new battery cables, esp if the ones you have are the least bit suspect. You can confirm a lot of stuff by reading the voltage at the fuse box with a load on like the ign key in the on position. If there is a high resistance somewhere there will be a voltage drop. Measure the voltage there with a multimeter. If its low then start working your way back to that starter connection. Another clue is with a heavy load like the headlights on the resistance will present with heat. So turn on the headlights, ign off, feel the connector at the starter, it should not be warm.
Some clarification is in order, there is a solenoid that electrically is a high current switch. one side is connected to the starter motor windings, the other to the battery thru a big wire, nothing in between.
there is also a smaller wire with a spade connector, this goes to the ign key, used to activate the switch and the engagement of the starter gear with the flywheel ring gear.
The wire harness has a large gauge wire white IIRC that shares the same connection to the solenoid as the big wire to the positive of the battery. This wire goes to the under hood fuse links via the wire harness.
The negative of the battery is connected to the starter physically and electrically by a mount bolt used to hold the starter to the transmission bell housing. All these wires need to be low resistance connections of a wire gauge suitable for providing the starter with the current needed to crank the engine without a significant voltage drop.
there are fuse links that are also separate from the fuse link boxes, they are the ones that feed the EFI directly from the battery terminals (not at the starter but at the battery post). they plug in and can have corrosion issues.