Maybe not directly related to the question, anyway this site allows calculating "what time it is" in a specific location on the Moon:
http://win98.altervista.org/space/exploration/moon/moontime.html
In this page, the moon day duration (29.53 days) is divided into 24 moon-hours; when sunrise terminator reaches specified point, local time will be 06:00; when sunset terminator reaches the location local time is 18:00.
But for a more precise indication of sun position of the Sun in the Moon sky, you can use this page to get the local Azimuth and Elevation of Sun using NASA Horizons data:
http://win98.altervista.org/space/exploration/NHUGUI.html
You must specify:
- COMMAND: Sun
- CENTER: coord@301 (specific location on Moon surface)
- SITE_COORD: longitude, latitude and altitude of site on the Moon
- TABLE_TYPE: Observer
For Vikram lander landing site (-70.90267, 22.78110, 0) this will result in this link, which gives:
- sunrise: 2019-Nov-03
- noon: 2019-Nov-10, Elevation = 17.8104°
- sunset: 2019-Nov-17
You can also get just rise/noon/set times by specifying YES for field R_T_S_ONLY and "1m" for STEP_SIZE, getting this link and these results:
Date__(UT)__HR:MN, , ,Azi_(a-app), Elev_(a-app),
*************************************************
$$SOE
2019-Nov-03 05:00,*,r, 86.6565, -0.2681,
2019-Nov-10 09:00,*,t,359.7476, 17.8104,
2019-Nov-17 13:44, ,s,272.5870, -0.2713,
$$EOE
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Note that sun is very low above the horizon even at noon because this specific location is close to south pole (70° latitude South).