All right, good job on bypassing the pressure switch and confirming the relay and pump are working. That pump is pretty easy to hear huh?
When I tested my safety switch with a multi-meter it was not installed and there were no 'wires' on it. I confirmed the solenoid side of the switch was connected to the power side (the circuit was complete). This makes sense because it is a 'Normally Closed' connection. The ignition side was not connected and this makes sense because it only should be connected if there is pressure.
What does this mean to you? The answer is yes, when you take the wire connected to the 'solenoid' wire of the safety switch (NC) and provide power to it from the battery the fuel pump should turn on. This assumes you have reconnected the power wire that you tested above. (And your switch operates the same as mine. I have the Holley switch).
If it does not there are a couple of possibilities. The first is you have the safety switch wired to the jeep incorrectly.
If you have the Solenoid and Ignition wires reversed the pump would power up when you turn the ignition 'on'. However, you used the choke wire which itself is regulated by a pressure switch. I think the next test is to take the wire that is connected to the ignition side of the safety switch and connect it to the battery power. The pump should NOT turn on if the safety switch is wired correctly to the Jeep. If the pump turns on then you need to double check your wiring. If the pump doesn't turn on then I suspect the safety switch is not working on the 'solenoid' side.
I assume the Jeep runs when you bypass the safety switch? You should get the jeep warmed up a bit with the safety switch bypassed and then reconnect the power wire to the safety switch. Be careful, it will be a bit warm. Then try starting the jeep. It should start, there is gas in the fuel bowl and listen if the pump is running. If it is running then the pressure side of the switch is working and you have it wired correctly. If it is not running you either have a bad switch, it is not wired correctly or the source you believe is 'ignition on' is not working or is not actually ignition on.
As Michel (letank) confirmed the other wire you are discussing is for the anti-diesel solenoid. This get's power when the ignition is on. If it is sparking then find where the wire has rubbed through and fix it. If you want a bit of information on how this system works let me know. The black part is the connector. The anti-diesel solenoid is a part common to many of the older cars which is why the wire color is not the same as the wire color on the Jeep. This circuit would be an excellent source for your electric fuel pump 'ignition' ' wiring. In my opinion it is better than the Choke wire since it is always powered when the ignition is in the 'on' position.