A tremor of a hand's thumb when holding an object

In August 2024, I began experiencing a tremor in the thumb of my left hand when holding an object. There was no tremor when the thumb was at rest.

The tremor occurred very sporadically in the following months.
However, towards the end of 2025, the tremor began to occur more frequently, to the point that in June 2026 I saw a neurologist for the first time.

I was initially diagnosed with Essential Tremor and prescribed PROPRANOLOL of 10mg.
I was asked to have an electromyography which did not show any nerve problems that could be the cause of the thumb tremor.

I took PROPRANOLOL for a month without any improvement in the tremor.
I was requested to have an MRI.
The report of the MRI indicated that basal ganglia spectroscopy showed changes suggestive of parkinsonism.

I was then prescribed PRAMIPEXOL 1 mg, one tablet in the morning and one at night.
I took the medication for a month without any improvement in the tremor.

I experienced however several side effects from PRAMIPEXOL.

I had episodes of daytime sleepiness, and dizziness together with muscle weakness when standing up after sitting or lying down.
The muscle weakness disappeared when I started moving, but the dizziness persisted throughout the day.

My neurologist reduced today the PRAMIPEXOL dose by half for 3 days and then asked me to stop taking it to assess whether the dizziness disappears.

What treatment change might the neurologist suggest?