Seems odd to me that these symptoms would team up!?
I agree with Magnet, must be a harness issue.
I'd recommend trying to check any if these faults with a multimeter to ground, will tell you if there's a break, or not
Doesn't sound too serious, probably a connector issue, hence the fine when cool state.
Have you had a check to ensure there's nothing looose/unseated with the glows?