Whose or Which?

They, whose advice I took, told me to rest more? Does this make sense?

To me, yes.

Does which make sense in this sentence?

In your original, ‘which’ is a relative adjective, the pattern being as follows: He didn’t get there till 10, by which time we had already left.
They used “peradventure”, which word is now archaic.
‘Mind your own business,’ he said, which remark made me very angry.
It started to rain, at which point we ran.

Saying “They, whose advice I took, told me to rest more” makes sense, I meant it’s understandable, not more (not the most elegant way of putting it.) “Those whose advice I took…” would sound better to me, but either of these sentences sounds rather formal, like, “Those whose passports I have…”; “The man whose hat I took…”

‘They which advice I took’ doesn’t work.

This makes sense because you have recast the sentence correctly. But the original question would need ‘which’ which is correct because it qualifies the whole sentence.