Recently, I had a pointer for a -3/-50% pirate base in Penelope's Star. After entering the system, it took about thirty real-time minutes and one month in-game time to find it! Very frustrating!
First, I check all of the planets, but no base. Then I checked the star; no base. Then I checked the asteroid clumps; no base. I captured one of the relays and waited a long time for a pirate fleet to appear. I went toward where it came from. Still no base! The only other place to check was the huge, entire asteroid belt at the edge of the system. Explored about a third of the belt, but no base. During all of that searching, I used Sensor Burst several times, all to no avail.
At this point, I spend one of my unused skill points in Sensors for Neutrino Detector, and loot the ruins at one of the planets for Volatiles. After trying to make sense with the blue aura, I finally found the base after traveling through another third of the asteroid belt, and it was in the fringe asteroid belt. The belt in Penelope's Star is huge!
Finding a base in Penelope's Star is like finding a needle in a haystack if the base is not near any of the planets, and searching all of the planets alone is already very tedious.
Other similar systems beyond core can have similarly frustrating results.
If there was any other way to destroy enemy bases aside from going there personally and killing them, I would have do so and spared myself much grief and babysitting.
Bar events that reveal the system the base is in should reveal where the base is in the system too. Spending thirty minutes finding a needle (base) in a haystack is frustrating and unacceptable.