Toyota Echo Radiator Flush Kits

I have a Year 2000 Toyota Echo. Want to install typical flush kit for
radiator. Not confidant about which hose to install tee on.

I do understand the two hoses coming out of the firewall for the heater
core, (left or right). But cannot see area where hoses go to engine and
cannot understand from instruction sheet if tee goes on hose to thermometer
or not. Plus, not confidant that I could ID thermometer.

As I look at the hoses coming out of the firewall for the heater core, one
is to the left other to the right.Can someone that knows the difference on
the model tell me which one to install tee in?

Also, how does a radiator flush work? Especially regarding the fact that
thermometer doesn't open until engine is up to temperature.

Regards, Piedmont