  We present a new approach to observationally constrain where the tails of
Jellyfish (JF) galaxies in groups and clusters first appear and how long they
remain visible with respect to the moment of their orbital pericenter. This is
accomplished by measuring the distribution of their tail directions with
respect to their host's center, and their distribution in a projected
velocity-radius phase-diagram. We then model these observed distributions using
a fast and flexible approach where JF tails are painted onto dark matter halos
according to a simple parameterised prescription, and perform a Bayesian
analysis to estimate the parameters. We demonstrate the effectiveness of our
approach using observational mocks, and then apply it to a known observational
sample of 106 JF galaxies with radio continuum tails located inside 68 hosts
such as groups and clusters. We find that, typically, the radio continuum tails
become visible on first infall when the galaxy reaches roughly three quarters
of r$_{200}$, and the tails remain visible for a few hundred Myr after
pericenter passage. Lower mass galaxies in more massive hosts tend to form
visible tails further out and their tails disappear more quickly after
pericenter. We argue that this indicates they are more sensitive to ram
pressure stripping. With upcoming large area surveys of JF galaxies in
progress, this is a promising new method to constrain the environmental
conditions in which visible JF tails exist.
