I also strive for instant response time (my wife hates that) and often, I'll already be working on a client issue that the servers emailed/paged me about by the time the client gets in touch (that definitely impresses them).
So, the typical pattern is this: I meet a new client, understand their needs, build a RESTful API back-end (Python, Django, Terraform, AWS), automate any internal processes and/or build internal tools, and then support their front-end team in building their web/mobile apps that consume the API.
Usually, it's a few days to a couple of weeks of full-time work, and then my hours drop off a cliff: either 1) the client's team takes over completely, or 2) if I stay on, any subsequent feature or issue takes just minutes for me to do, so then I'm back to square one, looking for the next client. So far, I've been lucky enough to make all the clients happy and have them become "clients for life," but that "life," added up between all the existing clients, is just a few billable hours a week.
Any advice for me to break this pattern?