Exactly, check continuity between the case of the plug to aircraft skin. If it's not grounded whatever radio is connected to it probably wouldn't function.
Normally the antenna is mounted with 4 screws to the aircraft skin.
This provides a GND for the antenna.
The antenna BNC connector (shield) is connected to GND inside the antenna.
Hopefully there is an identical looking plug at the transmitter, which connects the shield to the local ground there. The coax is a transmission line; the shield must be connected at both ends.
Most antennas route the shield connection at the BNC connector to the aircraft skin by either routing the signal to the airframe connecting screws, or to a flat metal plate on the bottom of the antenna which is in good contact with the skin. If you’re having trouble you might check the bottom of the antenna where it is in contact with the skin: no paint, no corrosion, there.