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Excellent question. From first principles: mars is about 1.5 AU from the sun. Using the intensity equation (inverse square law), Mars should receive about 1/(1.5x1.5) the amount of solar radiation, or about 44% on average.
Earth gets about 1400 W/m² hitting the top of the atmosphere, but most places on earth only see about 1000 W/m² after the column of air absorbs a bunch of it. Martian air absorbs almost nothing (being very thin), so you'd expect to see about 44% of 1400W/m² -- or about 600W/m².
A quick Google search for "mars solar intensity" shows a result of 590 W/m², so that is pretty close to accurate, from first principles.
So 60% as bright, if talking pure intensity. As you say, the human eye has a pretty responsive dynamic range, and this is quite an acceptable number.
For point of comparison, this is the difference between the sun at high noon versus the sun at 4pm for most of the world. On Mars, high noon would have a solar intensity more like 4pm on earth. No where close to your darkness experience with the eclipse.
With regards to the eclipse it would depend on how much of the sun is covered though. I'd assume it'd about the same as you'd get during a partial eclipse when the sun is 40% covered?
Effectively, yes