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In the image above there's a 12v+ bar connecting fuse 1 and fuse 2. Is the bar where it connects to fuse 1 terminal solid and not broken or compromised. The fuse 1 terminal has lost it's plating and probably badly pitted from the prolonged arcing, having a hard time keeping contact. The surface of a golf ball would be give you an idea.
I'm sure you have the dash illumination selector on the highest setting, but thought I'd mention it so you can double check. Pay close attention when the dash lights go on or off. Does it happen by itself or when you touch something like the turn signal arm, dimmer ring or other.
The buzzing is a tough one to diagnose over the net. There's a relay inside the steering column enclosure. You may opt to remove the enclosure and possibly the instrument cluster to pinpoint the buzzing.
If you mean Littlefuse, it's a good fuse and they've been around for nearly one hundred years.