There are very specific rules for Ragefire. Sirken clarified them for us months ago. He then ruled against his own very specific clarification so I had to show him where he already set precedent and that petition is back in the queue.
Here are the rules as clarified:
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The TLDR is you get 1 legit attempt or 20 minutes. Period. Suiciding to get the pearl handed in IS NOT an attempt. Switching over to different characters doesn't "abandon" the camp. You give the turn in party 20 minutes or 1 legit attempt.