Elinor was abandoned on the Artifact (when Picard didn't come back, he did what he thought was his duty and went in after him).
Elnor was frightened out of his mind.
No. Elnor was directly instructed by Picard to remain on La Sirena with Rios, Jurati, and Raffi. He refused the order, and transported over to save Picard's life. This is understandable, because he views Picard as the (absent) father he never had, and has sworn a vow to his cause.
However, he then abandons Picard at the end of The Impossible Box. Oh, he claims that he's defending Picard's exit, but Hugh says he has things covered, and Picard explicitly asks Elnor to come along. At best one could argue he's staying behind to stop Hugh from having to sacrifice himself shutting down the gate. But Elnor could have easily just waited and dispatched the next group of guards, then jumped through as Hugh shut down the gate.
In the end Elnor stays behind because the needs of the plot require one main cast member to stay on the Artifact, and for whatever reason, the writers decided on it being him. In staying behind however they kinda wrecked his character. I mean, he's only really been with the main cast on camera for Freecloud - so maybe a week or two tops? And he already leaves Picard behind?