how do I back up to my TC, when away from home?

It is extremely unwise to backup remotely to a TC.

Apple used to say specifically not to do it.. that piece of advice was removed although nothing IMHO has changed in the situation.. you are highly likely to break to the backup, unless you have 100% dropout proof internet and very high speeds.

When you are away from home it is far better to use a utility and backup just the files you need to the cloud.

You might want to read over this Apple support document about "local snapshots".

About Time Machine local snapshots - Apple Support

It is good when travelling to have a backup.. as lost, dropped and broken, or stolen items are fairly common.. but I think cloud is the solution. For current files only though. Backup to the same disk is a backup that is at as much risk as the original for the most part.

You are correct. I was not clear and did not mean to imply that "local snapshots" was a substitute for backing up to a regular drive or to the Cloud.

I used to travel with a small, rugged Lacie portable USB drive that I used for Time Machine backups as well as keeping a CCC "clone" of the Mac. The clone saved my rear end at least 3 or 4 times that I can recall.