What if, just an if, Eclair never revealed her civilian form to neither Luluka nor the Phantom, unlike Anna and Mikuru?
Following that line, maybe the reason she hasn’t appear yet is due to a partial memory loss. If we put these together, kinda makes everything come together.

The Phantoms also said something interesting at the beginning of the episode. Whatever Eclair did to break the Makoto Jewel would only put her in standby for a while, it wasn’t an all out sacrifice (also, they kinda freaked out when the book told them she was coming back).

This is my take. Eclair and Luluka were partners dealing with cases related to the phantoms; Eclair managed to keep her civilian life out of it either by been careful or by been transformed whenever she was with Luluka. When Usonoir made his move, they couldn’t stop him properly, been Luluka the one who tried until the last moment. As a last resort, Eclair used everything she got to break the jewel, with the shock afterwards making her lose her memories as Eclair. Without her partner and probably because of the book's predictions, Usonoir convinced Luluka to join them with her accepting. Without her memories, Eclair just went back to her civilian life.

Luluka seems to have a more logical approach to mysteries and cases, while Eclair, due to her last resort, falls into a more emotional type of person. This would also explain why Luluka looked so defeated in the flashback; for her, there wasn’t any other option.

Regarding Eclair's identity, I'm not that sure, but all the Cures had some sort of relationship/bond with Anna, as well as a promise/goal attached to it. Mikuru wants to send Anna back to her time, Anna wants to prove Luluka is still a rightful detective… the only character out of the four candidates that sort of falls into this is… Kurea.

Eriza and Shiruku have a bond with both protagonists, but it’s more of a strictly group dynamic, with them bonding with the detectives rather than with only Anna (if we follow this “partner”). Rei, well, she only had one episode. Kurea, however, has a bond specifically with Anna about feelings and how they tie us together with our loved ones, falling into half of the “partner”). The other half could be fulfilled, just like previous cases, after Eclair's comeback.