I have a question, what is the best method to fix my tubeless road tyre if I have a puncture while on a trip? I am searching for a fast method just to get home and fix it later.
The fastest way is to use tubeless plugs - bacon strips or worms. They are also used to plug holes in automobile and motorcycle tyres.
They are often sold in expensive bicycle-specific packaging, but the plugs itself can be bought much cheaper in bulk from sources directed to motorized vehicles.
The big advantage is that they are inserted from the outside, so you do not need to get the wheel off the bike. You just insert the strip (better covered by a vulcanizing glue, but follow the instructions) deep enough with a special fork and it remains stuck inside when you take the fork out. Before doing that you sometimes use another pick to prepare the hole.
The process is shown in this video:
If this is unsuccessful, try to insert another one, but you will likely have to deflate the tyre and insert an inner tube. Be careful for various old sharp objects stuck in the tyre. The sealant may have plugged their holes, but they can still puncture your inner tube.