I'm on the Island. After talking to Najoki I am slightly confused.
Spoilers Below
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It seems that I'm going to find Kachiko dead and I have to resurrect her. There was some mention of this needing to be done within a day of her dying. Does this mean I have to get through all the caves within one day? Or can I take my time, and rest a few times to regain my spells?

Exactly

Sleep before using rope. And you can buy some healing spell in Yoshomo casttle.

Many thanks for the reply. I found it out the hard way - by actually trying - that you CAN sleep during the elemental quest. I needed most of my spells to help me attack, not for healing. I suppose I could have gone back and done it (and also cleaned out each level) after rescuing Kachiko .... it would have been SO much easier!

Hmmm... I had Kachiko only as a mage but hadn't any trouble to clean areas without mage... Swords and bows have made their job

Summoned undead (especially high level) are immune to basilisks' petrification and they even distract them so you can have a couple of good fighters with Protection from Petrification take them out quick while the undead are fodder or extra melee damage. If you rest only for 8 hours you can make it too so your mage can restore the spells you need. Healing will be a loss but it is better for role playing in my opinion.

Or you can side with Bodhi next time...