I believe it should be noted that Mexico (location of the Toltec empire) is 8 hours behind Israel. Pretty much halfway across the world. Now I don't know about you, but to me, it seems like it'd be more likely for the Toltecs to have seen the Moon frozen in the sky rather than the Sun.
The Israelites obviously lived in a place where it was the Sun they witnessed as frozen. So the time of day when Joshua made his prayer must've been somewhere between sunrise and sunset. This varies on the season, of course.
According to Cambridge researchers (2017), the Sun and the Moon were frozen in between October and November (specifically October 30th). So the sunrise time had to have been at 6 AM (approximately). The sunset time had to have been at 5 PM (still approximately).
In Mexico time (CST), that is 10 PM and 9 AM respectively.
Mexico sunrise time for that date would be 7 AM, and sunset time would be 6 PM (still approximating).
The amount of hours where it is even remotely possible for the Toltecs to have seen a Sun frozen in the sky instead of a Moon is: 2 hours (7 AM - 9 AM). That means the probability of the Toltecs witnessing a frozen Sun is 2/15 or 13.3%. The probability of the Toltecs witnessing a frozen Moon instead of a Sun is 13/15 or 86.6%.
It is highly unlikely that the frozen Sun that the Toltecs witnessed the was same frozen Sun that Joshua asked God to stop, for those very reasons. That isn't to say impossible, it's just unlikely. There are so many variables involved that I simply don't know. And I can't possibly know for sure what happened on that day without being there myself.
If you want, you can try to see how I came to this conclusion, yourself. Please note that I approximated a lot.
So I saw the previous answer about the dates between the two events being separated by 1354 years. Although I find their findings to be likely (One thousand years a part sounds about right), there are always assumptions and approximations involved in the process to reach such conclusions. There are simply too many variables we don't know! Even in my findings I made assumptions and approximations. However, my approximations aren't that big of a deal for a time period of One day when compared to One thousand plus years.