If you have an engine monitor, the procedure is:
(1) Take off at sea level on a ‘standard’ day.
(2) Note the EGT of a cylinder (I usually monitor the EGT and CHT of my hottest cylinder) just after take off.
(3) During the climb, lean every couple of minutes to get to the same EGT on that cylinder (no need for absolute precision - close is good enough).
When taking off at higher density altitudes:
(1) Lean to until you reach the same EGT as you noted at #2 above.
Is there evidence to support the idea that the same mixture always gives the same EGT? (Actually we know it doesn't - one ignition inoperative will raise EGT, detonation will lower EGT, but lets ignore malfunctions.)
I would be slightly surprised if the EGT
was always the same - my guess would be that lower RPM, lower manifold pressure and lower air density would each lower EGT to some extent. That is just a guess though, I would be very interested in actual data.