To do the whistle-like style of overtone singing, the sides of the tongue are curved upward and held nearly against the upper premolar teeth, creating a seal with the roof of the mouth all the way around (with a small opening for air to pass).  With this in mind, try  singing "eerier" very slowly.   For higher overtones, move the tongue forward.

Vowel sounds and lip shapes are important in fine-tuning the overtones.  The lowest overtones are emphasized with tight "oo" sounds, while increasingly higher harmonic overtones can be heard as vowels change through "oo...oh...awe...ah...aa...ay...ee," and everything in between.

Another approach:  Use these vowel shapes without the modified tongue position.  This is effective for the lower harmonic overtones of the series (2-6).  You can also resonate harmonics 3-5 strongly by nasalizing the vowel transition from awe to ah.

The sequence of vowel shape transitions to emphasize overtones ascending the harmonic overtone series is "why."  "Yow" for descending the series.

Through experience you will find that more refined control down near the base of the tongue and in the throat allows one to isolate and amplify each desired harmonic overtone more effectively than just emphasizing tip-of-the-tongue or vowel techniques.

Overtone sing each harmonic through the series with your mouth completely closed, keeping the fundamental as steady as possible.  Harmonics 2, 3 and 4 are difficult to hear this way, and it is excellent for developing subtle listening skills.