i think you need to look at the existing planet with the ruins examine its properties and use them to find the new ruins. my 2p...
im doing it now, others help.
What do you think we have been doing. This was overdone on day 1 after the systems reveal but we have gotten nowhere, no concrete evidence what to look for. There are 5 million theories what we could look for.
Ranging from moons of ringed dwarfs to planets with moons to planets with 300K surface temperature to planets which are tidally locked to planets which rotate against their own axis. We have no concrete information what to look for. If we would have 2 or 3 planets to compare them and find a pattern, that would be easier. But with 1 planet it's impossible. But if you have any ideas, let us know.