It sounds more like the left switch gear is the culprit (it does control the lights including turn signals)
If its a carby model , check the right switch too (incase contacts are rusty inside the cluster & the terminal connector)
If in doubt, it is a good idea to replace the headlight relay and double check all front headlight H1 & h3 bulbs are 55w 12v (any higher will cause issues and melt harness)
The fact that your low h3 bulb even flicked for a second means the power does reach the bulb, so the “main harness” of the bike should be okay but don’t rule it out yet as it could be your last battle but hopefully not.
// Meditation doesn't mean you have to sit still....