My guess is that your console is designed to work with EIA tone signalling. (What you'd need for a direct connection to a mobile radio is what we call "E & M" signalling, which involves 4 pairs: Tx, Rx, PTT and COR (though most folks find using a VOX function to be more reliable that relying on a mobile radio to trigger a COR signal).)
In the absence of a channel card with E & M capability, your best bet is to get a tone interface module. This connects between the console channel card and the mobile radio; it takes EIA signalling from the channel card and translate it into E & M electrical signals for connection to the mobile, and vice versa. Tone control signalling comes in two flavors: 4-wire systems separate the Tx and Rx lines to and from the console, while 2-wire systems use the same pair for semi-duplex operation in both directions. You only need a 4-wire connection for full duplex operation, which by definition isn't available on a mobile radio used as a control station. So opt for a 2-wire set-up.