I don't think that the comparison TeX with a living being having eyes, mouth, stomach and bowels should be taken so seriously as to find an analogy with other body parts.
I like better the description Victor Eijkhout makes in “TeX by Topic” of TeX as operating on four levels (see pages 21 and 22):
The four levels are (corresponding roughly to the ‘eyes’, ‘mouth’, ‘stomach’, and ‘bowels’ respectively in Knuth’s original terminology) as follows.
The input processor. This is the piece of TeX that accepts input lines from the file system of whatever computer TeX runs on, and turns them into tokens. Tokens are the internal objects of TeX: there are character tokens that constitute the typeset text, and control sequence tokens that are commands to be processed by the next two levels.
The expansion processor. Some but not all of the tokens generated in the first level – macros, conditionals, and a number of primitive TeX commands – are subject to expansion. Expansion is the process that replaces some (sequences of) tokens by other (or no) tokens.
The execution processor. Control sequences that are not expandable are executable, and this execution takes place on the third level of the TeX processor. One part of the activity here concerns changes to TeX’s internal state: assignments (including macro definitions) are typical activities in this category. The other major thing happening on this level is the construction of horizontal, vertical, and mathematical lists.
The visual processor. In the final level of processing the visual part of TeX processing is performed. Here horizontal lists are broken into paragraphs, vertical lists are broken into pages, and formulas are built out of math lists. Also the output to the dvi file takes place on this level. The algorithms working here are not accessible to the user, but they can be influenced by a number of parameters.
Under this interpretation, the “gullet” would be the channel by which levels 2 and 3 communicate in both directions, for example when tokens sent to level 3 by
\uppercase return to level 2 after having been converted according to the values in the
\uccode arrays. However, I think this would add nothing to the understanding of how things work.
There is another aspect that's not covered by the living being allegory: the process whereby TeX sends to level 2 the macro replacement texts. Level 3 is responsible for storing macro definitions, which level 2 accesses at.
Finally, I would reject comparing the process whereby DVI or PDF files are produced, along with the
log and write streams, to another body part that I won't name. Such an analogy would be ridiculous.