Is “even when” a subordinating conjunction similar to “even though”?

[aatroxed]

"Even when he is sick, she works."

The first half is the dependent clause. Is it introduced by "even when"? Or is "even" an adverb qualifying "works"?

Typically you can move around adverb clauses. If so, which is the correct rewrite of the above to keep same meaning? (Subtle shift between each.)

She works even when he is sick.

She even works when he is sick.

Depending on the answers, is this grammatically sound? "When he is sick, she even works."

[Alan]

'Even' is indeed an adverb that modifies the adverbial element (i.e. the subordinate clause) that follows it. 'When' and 'though' are the actual conjunctions.