update: After reading @asdfex's excellent answer I think it is probably the right answer. I'll leave this here because it addresses the double light source hypothesis quantitatively, but I recommend that one reads the other explanation as it's probably the right one!
I'm going to put forward a theory and support it with the positions of the Sun and Earth seen in the sky of the Apollo 12 and 14 landing sites.
Seen from the Moon, the Sun is about 0.5 degrees wide while the Earth is about 2.0 degrees wide. You would expect the Earth to be at least somewhat near the Sun in the sky because the launches were timed to provide good sunlight on the Moon.
What I see in both of these cropped bits from the original NASA images is a shorter, weaker shadow that's about 4x fuzzier than the longer, stronger shadow. That certainly seems consistent with a shadow of Earthshine being shorter than a shadow of Sunlight.
The notations for these frames (see annotations of the images below) suggest that both were taken soon after landing. According to my plots of data from JPL's Horizons using the landing dates and lunar coordinates of the landing sites, the Sun was quite low on the horizon while the Earth was already at an elevation of about 60 degrees above the horizon and obviously remains fairly constant.
Light from both the Sun and Earth come from nearly the same azimuth (not much surprise there) so the shadows from Sunlight and Earthshine should point in nearly the same direction, about 270 degrees azimuth.
Apollo 12 Landing site Ocean of Storms 3.01239°S 23.42157°W
Apollo 14 Landing site Fra Mauro
Here are azimuth and elevations of the Sun and Earth as seen from these Apollo landing sites. Time axis is hours since
00:00 on landing day. Sun is solid red, Earth is dashed blue.
and the Sun is rising. So the angle difference will depend on the exact time of the photograph.
I don't have time today to check those but the explanation seems consistent enough for now. I'll get back to the timestamps tomorrow.
Plotted using inelegant Python 3 script (updated) https://pastebin.com/n1M1iSKy
above: Cropped from "Down-Sun with the dramatic washout." AS14-65-9211 at https://www.hq.nasa.gov/alsj/a14/AS14-65-9211HR.jpg found in Magazine 65 contains 14 pictures taken out the LM window after the landing..
below: Cropped from "LM shadow." AS12-48-7026 at https://www.hq.nasa.gov/alsj/a12/AS12-48-7026HR.jpg found in This Black and White magazine was used by Al Bean during EVA-2. The first 11 frames were taken from inside the LM before the first EVA..