I'd say it's not a double-headed relative clause, because it's actually
That is to say, 誰か is modifying the full predicate of 「行きたい人いる？」.
You can scramble to 「行きたい人誰かいる？」, which supports that 誰か is not in the relative clause.
However, even with this analysis, it is a somewhat confusing grammatical structure, since 行きたい人 and 誰か could both be seen to be semantically pointing to the same entity. This raises the question, are they both grammatical subjects?
I think it might be possible to see this as a "double-subject construction" (which is a poor name IMO, despite being used in the linguistic literature), where you can analyze the sentence as having a clausal predicate:
Note that it's odd to really use particles in a question sentence (it's more natural to use the zero particle), but I think it is borderline possible here as a linguistic exercise, and supports the double-subject construction analysis...
The following declarative sentence seems to work slightly better:
But even then it’s awkward.
The original word order is even less open to particle insertion IMO, though:
Due to the unnaturality of the above sentences, I think it's best to understand 誰か as an 'adverb' or 'modifier' in these sentences as opposed to a grammatical subject, even though it can serve as a grammatical subject in other cases (like 「誰かがいる。」 or 「誰かいる？」).
Supporting evidence for the adverb analysis can be found by drawing a parallel 何か, like 「何か質問ありますか？」 or 「何か質問あったら(…)」, where 何か is even more opposed to being marked by が.