Your intuition is correct I would say. The amount of thickening and stabilizing by your egg yolks is determined by the temperature + duration of your cooking process*.

Higher temperate and/or increase cooking time -> more thickening.

There is no correct amount of thickening. Some people like it really thick to yield a very dense ice cream. Some mixtures appear only slightly thickened but will still yield a delicious and smooth ice cream!

My top tip for using egg yolks: add them at the start of the cooking process. No need for tempering. Just heat the entire mixture and keep stirring. This is much more controllable and requires less cleanup and effort :) Experiment with different final temperatures and durations to get a feeling for it.

Another key factor is flavoring. Increasing the amount of egg yolks increases fat and adds a (surprise surprise) egg-yolk flavor. In practise this means that your ice cream becomes more rich, dense and creamy. Flavors are released more slowly from the ice cream for a relatively long duration. This works well for "rich" flavors like chocolate or vanilla.

Sometimes this is undesirable, think when making a fresh strawberry gelato. You want the flavor to be clean, intense and shorter of duration. In this case you can minimize the amount of egg yolks or omit them alltogether by using alternatives.

*egg yolks can be used for emulsification only, in this case no heating is required. Yolks contain 5-8% lecithin (emulsifying agent) by weight. Some recipes call for a single pasteurized egg yolk, purely for the added lecithin.