Let's get a quick bit out of the way.
CURRENT carcinoGeneticist [CCG] RIGHT NOW opened memo on board TEAM ADORABLOODTHIRSTY.
Ah, Karkat and his memos. Let's just skip to the relevant part.
FUTURE caligulasAquarium [FCA] 3:11 HOURS FROM NOW responded to memo.
Ah, yes. It's time to really hammer in that Eridan doesn't care about others.
FCA: hey sorry for bustin in on the memo but i cant get ahold of you youre not answwerin
CCG: OH FOR FUCK'S SAKE.
FCA: gams advvice is fuckin useless all he told me wwas to enjoy a bevverage
Yes indeed. This is the Eridan who was just dumped by Feferi, which is to say, the Eridan who just learned that Sollux died, and also that Karkat is so broken up about it he can't talk.
He is not even displaying the smidgen of caring for others that would have been him immediately trying to contact past Karkat when he learned about this. He does this only when, despite his best efforts, he still can't talk to Karkat about his problems. He's not even admitting here that there is a reason Karkat isn't answering, he's acting if Karkat and Gamzee are to blame.
CCG: NO, DUDE, DON'T DRINK THAT SHIT. IF IT WERE UP TO HIM WE WOULD ALL DRINK FAYGO AT ONCE IN SOME RITUALISTIC RAP CLOWN SUICIDE PACT.
CCG: BUT INSTEAD OF COMMITTING SUICIDE THE THING THAT WE ALL ACCOMPLISH IS BECOMING INSTANTANEOUS ASSHOLES WITH AWFUL TASTE.
FCA: i mean
FCA: its not evven that bad
FCA: its just soda but wwhatevver this isnt the point
CCG: THIS ISN'T THE VENUE FOR AIRING YOUR FUTURE PROBLEMS, COUNT SEA DIPSHIT.
FCA: i knoww i knoww
FCA: its just
FCA: i got a problem
FCA: wwith feferi
FCA: and im really kinda sittin here in bad shape about it emotionally speakin
Eridan really, really does not care about Sollux at this point in time. Granted, people can change, but Eridan/Sollux has always been on some impressively shaky ground. It's possible that later events did make him start to pay more attention to Sollux, but much more likely that it was all tied back to Feferi. Everything about Eridan seems to keep returning there. She's the only person he seems to care about instead of just faking concern to get them to agree to what he's asking at the moment.
Since there aren't other deaths until after the game (presumably Vriska's death and resurrection finished before most of them knew anything was happening), it's not clear if, say, the loss of Karkat would get more of a reaction since he uses Karkat for something, or if he'd just switch over to badgering someone else about his feelings instead. It's quite possible he'd act like this about everyone but Feferi...and, since he gets killed pretty soon afterward, even there it's unclear quite what his reaction to her death was. Erisolsprite, when we get there, adds a bit more on the subject but the nature of the beast confuses things.
Also on the continuing quirk front, Eridan isn't calling her Fef, perhaps to indicate the seriousness of his feelings, although he is using the rest of his quirk. What does this mean? Probably nothing and it's just that Eridan doesn't reliably use nicknames.
CCG: OK, WELL
CCG: I GET THAT, I HEAR YOU BRO
CCG: BUT THIS IS STILL NOT THE RIGHT PLACE FOR THIS SO I'VE GOT TO BAN YOU.
CCG banned FCA from responding to memo.
CCG: BUT SERIOUSLY JUST GET IN TOUCH WITH ME IN PRIVATE ABOUT IT, OK MAN?
CCG: WE'LL GET YOUR SHIT STRAIGHTENED OUT.
Eridan was also never lacking for support. Karkat is happy to devote his time to talking about Eridan's feelings, while Eridan could not care less about Karkat's own problems. This support does nothing to stop Eridan's eventual betrayal and string of murders, so it's really, really unlikely any further support would have helped.
Which doesn't mean there's nothing that could have changed things, just that lending an ear to Eridan's problems or offering him advice is not it. It makes sense if you think about it - the other characters repeatedly complain about Eridan's dramatics and we see here his problem is that his feelings are more important than anything else, and paying attention to him when he complains doesn't do anything to help. Maybe Karkat's later meteor rant about how if you want someone in a quadrant you need to care about them as a person was a start in the right direction. Or maybe not - it certainly didn't appear to have any impact at the time.
And that's it for Act 5/1 Eridan pesterlogs! Eridan has displayed awareness of other people's emotions but no actual empathy whatsoever, although he does seem to be relatively interested in their various relationships. He repeatedly expresses things that look like remorse at first but don't seem to impact his actual behavior and are immediately forgotten. He doesn't care at all about the death of another person. He is, however, either extremely emotional or, perhaps, just lacking any sort of perspective about how important even minor feelings are when they're his.
