Zach- look at the wiring diagram, and understand the components.
You've got THREE circuits involved in starting the engine... the FIRST circuit is the starter-solenoid circuit. You've got power from battery (at keyswitch) going through a series circuit of one or more safety switches and the starter solenoid, returning to the battery via chassis ground. (Check that chassis ground!). When you make up all the safety switches, and close the keyswitch, the solenoid should close with a nice, stout Click. Torin's test proved that the solenoid's coil is good, and that the internal shorting bar IS moving, but since you can't get same response with keyswitch, there's a problem somewhere between the keyswitch and the starter solenoid post. Start by looking for 12v at the keyswitch BATT terminal. Then, put your tester on the S, and turn the key to the START position. Move to each pin of the next safety switch, with the connector still on the switch, and the switch depressed, you should see 12v at BOTH sides of the switch. Continue through all switches, and finally check the post on the starter solenoid. When you get 12v at all locations, you'll have a continous circuit, and the solenoid coil SHOULD pull in... provided you don't have a ground-return problem between the solenoid and the battery. (Check the grounds!). Once you've done this, you should be able to hop on, depress the pedal, twist the key, and get a CLICK out of the starter solenoid.
Next circuit is the starting circuit. Battery cable carries 12v high-current capacity to one post of the starter solenoid. A shorting-bar inside the solenoid shorts the two large terminals together, and current flows from the second post, through wiring, to the starter-generator's big post. When the solenoid clicks, current flows through the S/G, (which will operate in 'motor' mode), to the engine block (as ground-return). From the engine block, current flows through a short bonding-cable, to the frame, through to the battery (-)post, for a complete circuit. Since you applied 12v battery directly to the S/G and got motion, the SG is functional... at least enough to make motion. Good connections and grounding are imperative, because this is a high-current circuit... any resistance in Either side of the circuit will drag the SG BAD. (Check those grounds!). Completing this, you should have a solenoid which clicks when you turn the key, and an SG that spins.