I know the general way in which cruise missiles work, but can they be programmed to terminate on a ‘lit up’ target (once they've gotten into the general vicinity via their geo-tracking capabilities)?
Nope. Cruise missiles are lat/long seekers. Various missile types have systems to seek infrared or RADAR reflections, but few have the capability to do more that that. When I flew Prowlers, we had HARM that could fly to an initial lat/long and then seek RADAR emissions. LGB's seek reflected laser or IR but not electronics.
The physical limitations are in the seeking method.
This is why everyone ever sent to gitmo or captured and released should have been implanted with a tiny gps locator, no wasted time or munitions when termination is desired. You know the same reason the socialists in this country want to do it to us.