Intercomp Alignment Gauge

Caster is read measuring the arc that the spindle travels as the wheels turn. This is why there is no way to read caster "live". You have to do a caster turn or sweep as you described.

Do the original caster turn, take your reading, make any necessary adjustments, do another caster turn, take another reading. That's how it's done. Even the most modern alignment machines cannot read caster live.