If your radio works without ignition - great, that's how the Coupe is wired from the factory. This does lead to battery drainage on newer radios, since they assume that the one of the power wires (red) is a switched, and the other (yellow) is providing constant power for memory.
Pic for reference: https://www.autofitkit.com/ebay/stereo-wiring-harness-adaptor.jpg
You don't need a new ISO connector. What you do need to do is to cut the red wire, and wire it to a switchable (ignition-on) power supply. There is one way to solve this
in the how to list, but personally, I would either run a direct wire from the battery, put a fuse on it, run it inside via relay to the radio. The relay can be switched on/off by using the cigarette lighter power, or some other switched live.
You can also use the existing cable coming to the radio, just using a relay, with signal from cigarette lighter or other live to switch it on/off.
This is to prevent frying the cables due to usage of both radio and cigarette lighter at the same time, since IDK what the cable gauge or fuse is on it.