We don't have any reason to believe there's a connection between Eclipsa's magic and the Blood Moon. The All Seeing Eye has been used at least two other times without any sign of the Blood Moon.
Both times the Blood Moon has apparently intervened were times when Marco in danger of losing Star forever.
In Bon Bon, this is more questionable because it seemed like Star was going to just straight up kill Ludo before Marco and Jackie show up and she's so distracted by them she loses control of her spell and almost gets sucked into the void. But it could have prevented an alternate or future danger for Star, or simply averted a future where Star never realizes/confesses her feelings for Marco and they simply grow apart, severing Starco (their bond) forever.
And now in Deep Dive, Star was in danger of losing herself entirely in the magic dimension. The Blood Moon apparently empowered Marco to contact her and snap her out of it.
This is more of a reach, but it may be notable that the All Seeing Eye exploded when Marco touched it. Star was able to touch it without any issue, it just rippled at her touch like water. This could be explained as Marco being far less experienced and attuned to magic compared to Star and simply losing control of the spell, but with the obvious flash of red when the spell is disrupted, it's possible that the disruption was deliberate interference to make Star realize Marco was in danger, forcing her to act quickly and reinforce that she still deeply cares for him, something we haven't seen a lot of this season. When she realizes he's safe, they hug for the first time since he moved to Mewni.
Looking back, this can also explain why the Blood Moon directed Marco to "help" Star in Bon Bon, even though doing so put her in danger. Saving someone's life certainly reminds you of how much you care for them, even if it doesn't immediately lead to love.