So from what i have tested, Jester will always have the radar in TWS mode and you will know this if you can see the radar returns on the TID. if the targets are too close together it will display as one contact on the TID and if you are trying to engage multiple targets, Jester will not push the next missile button in the RIO cockpit if he does not see more than 1 target. If you are playing in single player you can simply just hop in the back seat and push the button yourself and wait 16 seconds or so to launch the next missile, but ive found its a hit or miss whether or not the AIM-54 will track the second target.
you will know if you can launch another missile if you see the HOT TRIG light illuminate on the ACM panel.