  We have determined the proper motions (PMs) of 12 dwarf galaxies in the Local
Group (LG), ranging from the outer Milky Way (MW) halo to the edge of the LG.
We used HST as the first and Gaia as the second epoch using the GaiaHub
software. For Leo A and Sag DIG we also used multi-epoch HST measurements
relative to background galaxies. Orbital histories derived using these PMs show
that two-thirds of the galaxies in our sample are on first infall with $>$90\%
certainty. The observed star formation histories (SFHs) of these first-infall
dwarfs are generally consistent with infalling dwarfs in simulations. The
remaining four galaxies have crossed the virial radius of either the MW or M31.
When we compare their star formation (SF) and orbital histories we find
tentative agreement between the inferred pattern of SF with the timing of
dynamical events in the orbital histories. For Leo~I, SF activity rises as the
dwarf crosses the MW's virial radius, culminating in a burst of SF shortly
before pericenter ($\approx1.7$~Gyr ago). The SF then declines after
pericenter, but with some smaller bursts before its recent quenching
($\approx0.3$~Gyr ago). This shows that even small dwarfs like Leo~I can hold
on to gas reservoirs and avoid quenching for several Gyrs after falling into
their host, which is longer than generally found in simulations. Leo~II,
NGC~6822, and IC~10 are also qualitatively consistent with this SF pattern in
relation to their orbit, but more tentatively due to larger uncertainties.
