Sourcing of my opinions mostly based on Wikipedia and random hear-say.
The Antarctica already is an interesting case study. Different time zones are being used mostly due to territorial claims, but south of 80deg, UTC is dominant. Each base might be using their own, local equivalent of a day/night cycle. Connectivity is extremely limited; pastime Internet access makes 56k modems look like a luxury. Interesting reading: https://brr.fyi/
Near-term, we will most likely colonize the Moon long before Mars; shorter missions to lunar bases might happen in the upcoming decades. The Moon doesn't have a day/night cycle at all. It may have a similar effect on local, "human" timekeeping; people might talk with other local colonies as much as they do with mission control, and will rely on each other for immediate support. There are existing proposals for an LTC, which is both an engineering and a political challenge. One of the requirements stated in the current proposals already includes the handling of extended periods during which independence from UTC must be maintained - computers will run almost everything after all. Even access to the Internet will require a store-and-forward protocol, which will break the current webapp models. It won't affect how the years are being counted, but that's a lot of precedent even if just for technical and survivability reasons.
Any kind of travel from Earth to Mars will have to be scheduled years in advance, and takes hundreds of days at least for unmanned missions. The colonies will need a significant degree of independence for basic survivability: food, oxygen, recycling, production of maintenance parts, etc. Some may specialize and rely on each other. Even information travels for ~3m to ~20m, and there's a blind spot when the two planets are on the opposites of the Sun. Staff involved in existing missions are already carrying customized timepieces to track both planets' solar cycles. Human missions will likely be one-way trips for a very long time; several new generations may pass. We will have to figure out how to deal with the lower gravity too, which may require new science.
On the other hand, early colonies will likely remain subterranean (fun stuff like cosmic radiation), perhaps until we can figure out new materials. Big terraforming projects will require solving the unknown unknowns. I think it's too early to speculate, but eight millennia is a heck of a long time.
The Antarctica already is an interesting case study. Different time zones are being used mostly due to territorial claims, but south of 80deg, UTC is dominant. Each base might be using their own, local equivalent of a day/night cycle. Connectivity is extremely limited; pastime Internet access makes 56k modems look like a luxury. Interesting reading: https://brr.fyi/
Near-term, we will most likely colonize the Moon long before Mars; shorter missions to lunar bases might happen in the upcoming decades. The Moon doesn't have a day/night cycle at all. It may have a similar effect on local, "human" timekeeping; people might talk with other local colonies as much as they do with mission control, and will rely on each other for immediate support. There are existing proposals for an LTC, which is both an engineering and a political challenge. One of the requirements stated in the current proposals already includes the handling of extended periods during which independence from UTC must be maintained - computers will run almost everything after all. Even access to the Internet will require a store-and-forward protocol, which will break the current webapp models. It won't affect how the years are being counted, but that's a lot of precedent even if just for technical and survivability reasons.
Any kind of travel from Earth to Mars will have to be scheduled years in advance, and takes hundreds of days at least for unmanned missions. The colonies will need a significant degree of independence for basic survivability: food, oxygen, recycling, production of maintenance parts, etc. Some may specialize and rely on each other. Even information travels for ~3m to ~20m, and there's a blind spot when the two planets are on the opposites of the Sun. Staff involved in existing missions are already carrying customized timepieces to track both planets' solar cycles. Human missions will likely be one-way trips for a very long time; several new generations may pass. We will have to figure out how to deal with the lower gravity too, which may require new science.
On the other hand, early colonies will likely remain subterranean (fun stuff like cosmic radiation), perhaps until we can figure out new materials. Big terraforming projects will require solving the unknown unknowns. I think it's too early to speculate, but eight millennia is a heck of a long time.