Alternatively, you may be able to use the direct URLS to the API (rather than the ‘modified nice looking ones’) as outlined in:
https://community.suitecrm.com/t/request-to-api-return-404-error/65657/29?u=anothermouse
This means that you can avoid the shortened https://mysite.com/Api/access_token and instead use the full path https://mysite.com/Api/index.php/access_token
Similarly for using the V8 Api, replace https://mysite.com/Api/V8/module and instead use the full path https://mysite.com/Api/index.php/V8/module