Short answer
What you rank for decides what you get called about. To change the mix, write properly about the work you want and briefly about the work you do not, tighten your service area, fix your categories, and let your pricing filter the rest.
Most plumbers I talk to do not want more calls. They want different calls. Fewer 2am blocked drains, more bathroom work. Fewer twenty minute jobs on the other side of town, more of the ones worth the drive.
That is a marketing problem, and it has a marketing fix.
Why you get the work you get
What you rank for decides what you get rung about.
If the only substantial page on your site is about emergency callouts, emergency callouts are what you will be found for. If your profile lists drainage as a category and nothing else, drainage is what the phone will bring you.
It is not random. It is a fairly direct reflection of what you have told Google you are.
Lever one: write properly about what you want
Build a real page for the work you want more of, and keep the work you want less of to a short honest paragraph.
You are not lying about anything or refusing jobs. You are simply giving Google far more to work with on one than the other. A thorough page about bathroom renovations will out-rank your own thin mention of blocked drains, and the mix shifts.
This is the single most effective lever and it is entirely within your control.
Lever two: tighten your service area
If you have nine suburbs listed and three of them are a forty minute drive for jobs you resent, take them off.
Plenty of plumbers list everywhere they could theoretically go rather than everywhere they want to go. The profile then does exactly what you told it to.
Lever three: fix your categories
Secondary categories on your Google Business Profile open you to specific searches. That works in both directions.
If you have Septic System Service listed from when you took one job in 2019, you will keep getting rung about septic systems. Take it off. Add the ones matching the work you actually want. Categories are worth getting right because they do more work than most settings on the profile.
Lever four: let pricing filter
Putting your callout fee on the site loses you some calls. That is the point.
The calls it loses are disproportionately the ones ringing around for the cheapest quote, who were unlikely to book you and were going to take twenty minutes of your time finding out. It is a blunt instrument and it will cost you some good jobs too, so it is a judgement call rather than a rule.
How to know if it is working
Track what type of job comes in, not just how many.
This is one of the more useful things that falls out of proper reporting. If you can see that hot water work has gone from a fifth of your enquiries to a third over three months, you know the page work is doing its job. Without that, you are going on whether last week felt better, which is not enough to make decisions on.