That connection to the antenna requires a very good ground at the tuner and even then the unshielded part of the coax is now part of the antenna and can radiate. If you have another section of coax with a connector on one end take about 3 inches of the jacket off the antenna end, leave the shield, un-braid the shield and twist it, cut it to about 1 inch long and crimp a ring lug on the twisted shield, unscrew one of the three nuts that hold the insulator to the car body, put the ring lug on the screw and reinstall the nut, then hook the center conductor to the antenna as you have the one now. It should look something like this:
Sorry about the crappy pic, that compartment is small and can't get the camera far enough to focus properly.
From the Manual:
read the part in bold
JUMPSTART, OR “REAL HAMS DON’T READ MANUALS!”
Ok, but at least read this one section before operating the Z-100Plus: Turn off power to your radio.
Connect the antenna jack on the transceiver to the “TX” jack on the Z-100Plus, using a 50 ohm coax cable jumper.
Connect a 50 ohm coax antenna feedline to the “ANT” jack on the Z-100Plus.
Power up the transceiver and select the desired operating frequency.
Select AM, FM, CW, or PKT mode, and then key down to transmit a carrier1.
Push and hold the TUNE button on the front of the Z-100Plus for one second (until the Tuning LED comes on), then release.
Wait for the tuning cycle to end (red LED goes out, 1 - 6 seconds) and then un-key. Restore the transceiver to the desired operating mode.
You’re ready to transmit!