I have searched many a page on wikipedia, the official GS1 specifications, but have yet to find a definite answer to the question
What is the actual HEX / binary value of the GS1 FNC1 character?
There is much information about how to use the GS1 identifiers, how to print the barcodes with ZPL and how to encode the FNC1, but I want to know the actual HEX value of that character.
The special function characters such as FNC1 through FNC4 belong to the class of "non-data characters" that can be encoded within various barcode symbologies but with do not have any direct ASCII representation in the decoded data stream. Each symbology that supports such characters has a different scheme for encoding them in its internal representation quite distinct from any byte-orientated character data.
The FNC characters serve both as flag characters (indicating something special to the reader) and as formatting characters (modifying the meaning of the encoded data). As such they are not intended to be transmitted directly in the data received by the host system from a basic barcode reader, although in both cases they may have an "effect" on the transmitted message.
The usual purpose of each of the FNC characters are as follows:
Be aware that they may not all be available in certain barcode symbologies and may even be specified in different, non-typical or overloaded ways. By way of example, in the DotCode symbology the role of FNC1 is inverted for messages beginning with two digits, FNC2 is overloaded to declare ECI indicators characters when operating in extended channel mode, and FNC3 is overloaded to provide "symbol separation".
The individual barcode symbology standards must be consulted to determine which FNC characters are supported and how the transfer protocol defines the communication between the reader and the host when a symbol of that type is scanned.
Upon scanning a barcode the symbol's internal data is typically decoded then transmitted to the host over a basic channel (e.g. keyboard wedge) as a sequence of bytes to be interpreted according to the Latin-1 character encoding. The FNC characters cannot be represented in such a manner and are excluded from the data stream, however their formatting effect on the data remains.
For instance, the standards for most symbologies specify that when an FNC1 character is being used in its role as a field separator in data conforming to GS1 Application Identifier Standard Format it should be decoded and transmitted as GS (ASCII 29). Explicitly stated, the formatting effect of a FNC1 character used as a GS1 Application Identifier separator is to place a GS character at the end of the variable-length field. But in other roles (such as when FNC1 is used in "first/second position" as a flag character and with non-GS1 formatted data) there is no formatting effect on the carried data and therefore no ASCII representation during decoding.
Another instance of the special function characters having a formatting effect on the data is with symbologies that use FNC4 to extend their reach from 7-bit ASCII into extended ASCII as described in this answer.
A subtle technical point is that the data transferred to the host is often prefixed with a short symbol indicator header known as a "symbology identifier" which denotes the type and usage of the symbol from which the data is being read. This is often modified by the presence of otherwise invisible flag characters within the symbol data, for example to indicate the presence of GS1 formatted data with "FNC1 in first" or to indicate reader programming mode when FNC3 appears anywhere in the symbol. The details are symbology specific.
Placing an FNC character in a barcode message
Within barcode symbol software, encoding an FNC character in a symbol's internal data is accomplished via a software-specific "escape mechanism". Each application or library has a different way of accepting these non-data characters within their input. For example, to use FNC1 in its typical GS1 structured data role for the data "(01)00312345678906(21)123456789012(30)0144" you might see the FNC1 characters escaped as {FNC1} so that the input looks like {FNC1}010031234567890621123456789012{FNC1}300144.
Some libraries will even use a set of regular or extended ASCII characters as placeholders for the FNC characters, but these are arbitrary representations and it is a mistake to consider them to be actual ASCII values for these non-data characters.
Aside: In addition to FNC non-data characters, there are other non-data characters commonly supported by barcode symbologies that have no direct ASCII representation but affect the overall message. These include macro characters (that wrap the message data in a data character "envelope"), and ECI indicators that require the use of a transmission protocol beyond the typical "basic channel" mode but which enable the use of extended character sets amongst other enhancements.