When I opened my game this evening I found Tonga, my chief, had died of old age at 75. I therefore went through my villagers one by one until I found the new chief, Paka. I started with the youngest and - of course - Paka was the oldest in the tribe, at 76.
I also only needed one key to open the door. I got that, and it started raining just as the door was opened. I put the villager who got the key on the sun dial to move it, but there was of course no beam of sunlight to activate the final puzzle. Then the sun came out ...
I looked round and there was the skeleton of Paka lying in the amphitheatre. She must have died at the same moment the Prince and Princess appeared. I feel sure it must have been shock, although the ROD said old age. She'd only been chief for about 10 minutes.