A plumber does not need a shop front to be a real local business
Google describes a service-area business as one that visits or delivers to customers directly but does not serve customers at its business address. Plumbers and cleaning services are examples Google gives itself.
If customers do not come to your address, the profile should be set up to reflect that rather than making a home or office address look like a customer-facing shop.
Do not show an address customers cannot actually visit
Google says that if you do not serve customers at your business address, you should remove the address from the public Business Profile and use service areas instead.
That matters for mobile nail techs, cleaners, trades and other businesses run from home where the home is not a place clients are meant to turn up.
Use the areas you genuinely serve
Google currently lets service-area businesses choose up to 20 service areas using cities, postal codes or other areas. It also advises keeping the overall area reasonably close to where the business is based.
Do not add places simply because you would like to rank there. Use the places you genuinely travel to and can realistically serve.
What a customer still needs to understand
Hiding a non-customer address does not mean leaving the profile vague. A customer still needs clear services, contact details, hours, areas covered, reviews and useful proof of the work you do.
For a plumber that means the jobs you take on and where you travel. For a mobile beauty business it means the treatments, booking route and areas you cover.