My father's enlistment document lists his civilian occupation as: bottom puller code 8-61.01. What does that mean?
A bottom puller is an occupation in the manufacturer of shoes, so someone who worked on the soles of the shoes, but not likely in the assembly but literally making of the soles. It was likely someone else's job like a tacker to tack them on.
At one point in history before heavy automation people had specialty occupations that were specialized to certain specific parts. Shoe and boot making is a good example where they used multiple sub-categories and then as automation ramped up they consolidated it simply into shoe maker and / or the sub-job code and titles changed with the technology and need for human labor in the process.
This sub-occupation list for Shoemaking in the US lists several "Puller" sub-types which compliments the list above.
In this particular 1920 list of occupations example you can see there are multiple "bottom" related occupations and this has nearly 4 densely packed pages of sub-shoe making occupations. You will also find many other "bottom X" occupations in it related to clothing industry and for another example they brake down "feller" which area of the a coat they work on (collar, sleeves, bottom).
This 1939 list of US Occupations thought completely re-uses that sub-code for another shoe making sub-type. An anti-sqeek filler, which per this link is "Applies liquid coating to shoe parts, or cements cushioning material between parts, to prevent squeaking due to friction or wear. 2) Brushes coating of liquid chalk, paraffin, or wax on parts, such as heel bases, flares, and outsoles."
This 1946 document from North Carolina has that specific code of 8-06.01 as a Piercing Marker, but the codes vary by region as denoted in the comments.
Knowing the specific location AND date of the information the specific 'duties' of the occupation could be determined based on shoe making technology of the time period.
From the format of the code itself, I deduce that the original source must be WWII enlistment papers from the United States. I agree with the earlier answer that code 8-61.01 is likely to be a shoe industry designation.
This style of code was still in use in the late 1950s, as can be seen in this reference work: Handbook of Representative Industrial Jobs for Blind Workers (1960). Code 8-61.01 is listed as "sole wetter" -- someone who treats the cut soles of shoes with a water and softener solution so that they will be more flexible for working.
For earlier forms of occupational codes used in the United States, see Dictionary of Occupational Titles Part III Conversion Tables (1939), which (as the title suggests) allows occupational analysts to convert from an older style designation to the newer code.
Wikipedia's article on the Dictionary of Occupational Titles says:
The Dictionary of Occupational Titles or D-O-T (DOT) refers to the defunct publication produced by the United States Department of Labor which matched job seekers to jobs from 1938 to the late 1990s. It was then rendered obsolete and replaced by a database which is largely informed by people who have direct experience working in each occupation, the Occupational Information Network or the O*NET. The last government version was published in March 1999 as two volumes with additional information related to the O*NET database.
(The reference cited by Wikipedia for this paragraph was a PDF article from 1999, "Replace with a database: O*NET replaces the Dictionary of Occupational Titles.) See the Wikipedia article for more uses of the Dictionary that may be relevant in questions about family history -- e.g. its use by the Social Security Administration.
"Recently on QI they listed occupations given on old census forms and nobody knows what these are now, some may have been dialect terms or some job spacific terms. I am sure some people were too specific "tin plate worker" would have been enough but "bottom puller" was what he was known as at work!"