One high beam works one doesn't, gauge cluster does not light up

Sounds like you need to look for a bad ground for the passenger headlight.

check for a damaged wire for the low beam. Also wouldn't hurt to check the ground wire as the high beam will try and ground through the low beam but not visa verse

You have lost the ground, evidently on the left side. The lamps act that way because one of the lamps is grounding through the elements of the other lamp.

This is usually caused by a failed front control module as this unit controls the lighting on the vehicle!
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These trucks are known for bad multifuction switches.
the switch that i talk of is the signal switch , the handle is the switch, it bolts to side of steering column . this switch controls the signals and the headlights and high /low beams. the other thing is the headlight switch connector, the connector some times goes bad and starts to melt or just comes out of the connector. you will need to remove the cover to steering column, the screws are located under the bottom cover in holes. remove cover and check connector and then test for power if you have power going into switch but not coming out then switch is bad.

the last thing is to make sure the bulbs are good , make sure the headlight bulbs are good , and also the driving light bulbs, test for power at the connectors to those lights to.
You will need to do a little testing to find the problem.

Did the low beams go off?.. If not, it sounds like you have a bad switch.

The blinking light is telling you that you have a headlight out, if you look the service light should be coming on when the light stops blinking.
Replace the head light and all should be fine.

most likely the hi lo switch

DID YOU CHECK THE BULBS?

Don't know that much about 99 Surburbans but you may won't to see if you could just unplug it from the cluster or maybe see if thiers a fuse for your lights that you can take out