I'm sorry, but amoebas are cells and neurons are cells. The fact that neurons are specialized is not evidence that other cells can't learn or have other sensitivities, such as photosensivity or magnetic orientation.
The "will to live" is voluntary, i.e. willful. Specialization, function and capability are involuntary, i.e. circumstantial.
Since you brought it up, it is fascinating to note that the “will to live” accrues to the autonomous organism or collective (in the case of ants and bees). All of the composite molecular machinery (cardiovascular, neural, digestive, etc.) integrates to that purpose for the organism or collective.
The “theory of evolution” does not address these things – the will to live, the autonomy, the integration of function to purpose, information (successful communication) and semiosis (encoding/decoding).
All of this is related to the study of complexity in biological systems - an endeavor of the mathematicians who have been invited to the evolution table. That may have been a “fatal attraction” since these are also related to the objections raised by the Intelligent Design supporters whether they see the Designer as God, aliens (panspermia, cosmic ancestry, astrobiology) or collective consciousness.