While someone operating a lunar rover (or an automatic one) would use headlights for safety, if you got lost at night and your power was batteries, you would need to nurse them for two weeks until sunrise.
Driving by Earthlight might be fun, necessary, and helpful for low-power autonomous rovers since reducing power for headlights might allow a longer range for a given battery mass.
Therefore this is helpful to know and potentially important to know!
- Now large would the Earth be, and how bright, with comparisons, would it be? How brighter or dimmer would it be from the full moon, or a lamp?
- Can you read under the light of the Earth?
- And I know it would vary, so how bright would be at half full, or quarter full?
These are good questions and relevant to the experience of future Moon colonists, where dwellings and vehicles will have "Sun roofs" and "Moon roofs" but they'll be called "Earth roofs".
Since some folks have "cast shade" on this question of Earthlight, I'll post this answer as partial before a possible closure then continue to work on it.
There are relevant answers to several questions in Astronomy SE:
- How bright is the full Earth during the lunar midnight?
- How many times brighter would full-earth-shine appear to people standing on the moon, than full-moon-shine does to people on earth?
and here in Space SE there are answers we can draw from as well:
@DavidHammen's answer to the 2nd question includes the following:
The full Earth as seen from the Moon is, on average, over 40 times brighter than is the full Moon as seen from the Earth. Reading a newspaper on the Moon at night under a full Earth would be a piece of cake compared to reading a newspaper on the Earth at night under a full Moon.
While there's no supporting calculation given, on matters of Space Exploration DH's opinions and assertions are pretty much "99 & 44/100% reliable" to borrow a phrase from space history and use it out of context for the purposes of levity. In reality, over the last 7 years and 5 months I have never seen a DH factoid I found fault with - and when I doubted them I followed up and was reassured.
So we can probably safely say that yes, you will often be able to read a newspaper on the Moon when illuminated only by Earthlight. Of course it may get pretty dim during new Moon and disappear when you're experiencing a lunar eclipse (penumbral or umbral) so it's probably not reliable.