An A1 certificate is evidence of which country’s social-security legislation applies in a cross-border situation. It is not a general work permit and it does not settle income tax.
Facts come before the certificate
The competent institution may need to know your residence, employer, expected work split, assignment period and whether you normally work in more than one state. Keep a realistic record of workdays rather than relying on an informal label such as “occasional remote work.”
Different routes may apply to a posted worker, a person normally active in two or more states, or an employee covered by an arrangement concerning cross-border telework. Ask the relevant institution or insurer which route fits before assuming a form is merely administrative.