Is there any evidence for dark matter besides just its gravitational effects?
What I’m getting at is...why are we so quick to assume it’s any kind of “matter” at all rather than just some unexplained fluke of gravity?
There is substantial evidence (e.g. from measurement of the cosmic microwave background) that the universe is almost flat - that the energy densities in the universe sum up to be almost equal to the critical density.
The contributions due to neutrinos and photons are almost negligble at the present epoch. Dark energy appears to contribute about 70% (which is in concordance with observations of high redshift supernovae). That leaves 30% to be supplied by matter. But when we add up all the contributions of matter that can be detected, we only get to around 1-2% of the critical density. There appears to be lots of matter that we cannot see. Furthermore, we know from big-bang nucleosynthesis calculations and measurements from which the primordial He, D and Li abundances are inferred, that "normal", baryonic matter contributes at most about 5%. Therefore we are left with accounting for 25% of the energy density of the universe by something which cannot be seen and is non-baryonic.
I believe this line of argument is quite separate from the dynamical/gravitational arguments for dark matter, based on the rotation of galaxies, the motion of galaxies within clusters and the formation of structure.
Short answer: no.
Thus far all evidence for Dark matter is based on gravitational interactions. Be it from galaxy rotation curves, galaxy cluster dynamics, gravitational lensing, or cosmology. This tells us that if it is caused by matter, this matter has little or no interactions with light (or the EM-field in general). That it is matter, is at this point still a hypothesis (however this hypothesis is consistent with a now wide spectrum of observations).
People have also tried to explain the observed phenomena using modifications of graviational physics. The most well-known example is "modified newtonian dynamics" or MOND, but there are other variants as well. These alternative theories typically struggle to explain some observed phenomena such as the "bullet cluster" (an observed collision of two galaxies with a significant displacement of the gravitional mass from the center of the collision, as expect for dark matter halos, but not necessarily for modifications of gravity), or the recent observation of a galaxy without dark matter (which is challenging to explain with a unviersal modification of gravity). Nonetheless, proponents of the alternative theories usually find ways to incorporate these observations.