How to run both
Leave Fathom exactly where it is. Add the Tiny Funnel script tag next to it, then open your own site in setup mode and click through the flow you care about: the landing page, the pricing page, the signup form, the welcome screen. That click-through is the funnel, and there is no event code to write and no goal to configure first.
Nothing about the two scripts conflicts. Both are cookie-less, both are first-party, and they are answering genuinely different questions, one the whole site at a glance, one a single flow in depth, so keeping both is not a transition state. It is a reasonable place to stay.
The layer Fathom does not have at all
Fathom is deliberately aggregate, and it does not try to be a funnel tool. Custom events are flat counts, and the dashboard shows zero personal information by design, which is a considered privacy posture and suits a "check it once a week" habit well. There is no sequence of steps behind a goal, so when a number moves there is nothing underneath it to read.
Tiny Funnel is that layer. Any visitor in the funnel can be opened and read end to end, return visits included, down to the step where they stopped, and a step can be a page state, a click, or an event your backend posts when the money actually moves, attached to the visitor who caused it. A visitor the script tag has never seen cannot be started by a server event, so the journey always begins in the browser, but it can end in your webhook handler.
The short version
Keep Fathom for the site. Add Tiny Funnel for the funnel Fathom was never built to draw: where each cohort of visitors comes from, how far they get, and which of them buy. Adding it costs $10 a month per funnel, and neither tool uses a cookie.
