Any way to find number of neurologists by country?

3 digit ISCO88 won’t have the level of detail I am looking for - any other sources I can use for this?

I am unaware of any publicly-available data resources that provide country-level employment data for ISCO codes more detailed than the first 3 digits. The online databases for the International Labour Organization and OECD do not appear to provide more detail than the IPUMS-International microdata. You might have more success trying to find this information for each country separately.

Sorry that I could not be of more direct assistance.