As an amateur astronomer, I intend to perform a few simple experiments during total solar and lunar eclipses. However, I am not aware of all the parameters that can change during these eclipses and hence can't chalk out any experiments. Could anyone suggest some ideas?
Since the edge of the Sun's disk as seen from Earth is slightly redder than the center due to limb darkening and this effect is stronger for blue light than red, a partial solar eclipse covering more limb than center will cause the remaining ambient light on the ground to be slightly bluer than normal, until it completely covers the center but not some edge, at which point it will be slightly redder than normal, where "normal" refers to the light of the unobstructed Sun at the same position in the sky (and other atmospheric factors being the same).
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The colors within the Earth's shadow seen on the disk of the Moon are different for each eclipse because they originate in Earth's atmosphere. There have been some unusual ones due to recent volcanic eruptions which spewed dust and gases high into the atmosphere where they remained for months or years. You could photograph Earth's shadow on the Moon at regular intervals throughout a lunar eclipse using several narrow-band color filters over your camera to make a coarse spectral analysis, or even make a DIY spectrometer from a DVD or a prism (search for these projects elsewhere) and record a spectrum proper.