Dizziness and vertigo generally are not caused by upper cervical disorders except for vertebral artery syndrome. The vertebral artery threads through the first and second vertebra. It is rare but there can be a type of disorder where rotation of the head can temporarily cut off this blood supply causing the symptoms you describe.
The way to diagnose this disorder is with a CT angiogram with variable head positions while doing the scan. If the vessel is patent (open) in certain position but cut off in other positions, this would confirm the presence of the disorder. Having return of dizziness and vertigo symptoms with this “cut-off” sign present is very strong evidence of vertebral artery syndrome.