The broiler lights but then goes through the re-light cycle, i.e. stays on for about 10+ seconds, then some igniter clicking (about 6 times), gas valve closes, wait ~ 30 seconds, repeat. The oven/bake burner is working fine.

Here's the strange part. If I turn on the oven/bake to the lowest graduated setting (200F), let the oven heat to temp, then turn on the broiler, it stays on.

My thinking is it's the flame sensing in the broiler (it looks to be a single rod igniter/flame sensor). I've read a bit about this, i.e. flame rectification etc. The igniter/sensor rod is clearly in the flame of the broiler. I've tried cleaning it lightly with some emery cloth to no avail. It seems the higher temperature fixes the flame sensing for the broiler. Any and all help greatly appreciated.