Something I noticed earlier today—examining the Thargoid War information for previous Titan systems such as HIP 8887, and looking very closely at the background within the dead rings, there is a very faint red heartbeat signal still present. Even if the Titan is a visible shipwreck when visited, something is still pulsing a signal with the unmistakable double-beat of a heart.
That is the case since Taranis was destroyed - I'm thinking it is more like a "signal" of sorts - green and 'calmer' when a Titan is fully operational, it switches to being more agitated once down to four hearts and changes from green to red. It fully becomes red when the "meltdown" starts and the 'signal bar' is most active during that period. What exactly it does mean during those first three phases is unclear, so I'm basing my assumption of "signal display" off of the 'Titan destroyed' stage where it, as you've observed, is very faintly active.
Residual emissions from the wreckage - however, I have heard people report that Scouts patrolling the wreckage early on would immediately react to attempts at retrieval of the bits and pieces which can be shot off from the Titan remnant. And, if the other Thargoid shipwrecks we have seen to date are anything to go by, something may well remain active, to a degree*. If extremely unlikely it has any role to play in the war from here.
And on this subject - while I haven't yet made a comparison, being there at Oya's destruction gave me the impression it made a different 'sound' to Leigong and Taranis prior to the explosion. Of course, I'll be there to verify its (exact) status when its wreckage does become accessible... even though I'm sure someone will get to it before me.
*I recall reading somewhere that tests of the enzyme missile rack on Thargoid shipwrecks resulted in those remnants neutralizing the enzyme despite being dead for over a century. Likewise, even relatively inert Thargoid biotechnology seems to be rather resilient to decay... looking at how we can find the signs of battle from millions of years ago around Guardian sites. One has to wonder how long the Titan wrecks will remain if not picked apart entirely, or if they don't de-orbit and crash on the ammonia worlds which they orbit(some of which have dense enough atmospheres to probably just crush the hulls before they can reach the surface - without any data to tell what pressures a Titan hull, fully or partially intact, can resist).
I too have been wondering if we actually get to attack all eight Titans, or eventually the survivors will be smart enough to retreat. Surely all eight won't just sit there and take it? Not very smart for a species that's supposedly been starfaring since before humans discovered fire.
What the remaining Titans do or how they respond depends entirely on whatever purpose they were said to be here for, which is still just as up in the clouds as before. And reducing those things to piles of rubble doesn't really make for a particular ground to understand either. Beyond that this elusive goal is apparently worth throwing three(or more) giant ships under the bus.
If their goal was to search for something within the Bubble, even just moving throughout it would have achieved better results than remaining stationary at the edges of human space and - partly - ineffectually fighting over the same space repeatedly. Or continuing the regular modus operandi while those Titans are no longer quite as invulnerable as before. If the whole goal was just to plant down those spires, I'm not sure that would have needed eight Titans, and they could also just have put them down and left the towers standing (always only in unpopulated space, I might add) as we scratched our heads about whatever they are really for. Sure doesn't seem like they are extremely vital or that impactful on damage resistance - Oya continued to Very High with 9 controls and 2 spires(one of those reactivated, but readout said it was the same as the other).
And that other elephant in the room, the abductions. If they were hoping to use them as a discouragement from Titan destruction... can't say it's working too well.
(I somewhat doubt that all 8 will actually go down, though there would also probably be some annoyance at not getting the full Titan killer decal or whatever if that were the case.)