Yes, that is indeed a clue.
The BF #### can be used to identify where the gauge was originally used. I do NOT have the secret decoder book for part numbers. However, Googling for the part number I found the two links below.
First see eBay and look for item #290328716790 That should be the same type of gauge you have based on the part number you listed.
More importantly, visit this web page:
https://www.mgb-stuff.org.uk/fuel.htm
Search the page for "2223/00" and you'll come to a section that says the gauge you have is for MGBs made after 1967. That means it is for cars WITH the voltage stabilizer.
Look at the back of your gauge. If (excluding the rust) it looks like the back of the gauge shown in the second link above, the gauge you have is for later cars. You will notice it has two "screwdriver slots" below holes on the back of the gauge.
The back of your gauge should look like this:
https://mgaguru.com/mgtech//electric/pics/fg_289.jpg
(Thanks to Barney Gaylord for the picture).
Notice that instead of the screwdriver slots there are two additional little studs (with nuts) poking out the back of the gauge. These little studs pass through short slots. That's the type of gauge an early car without the voltage stabilizer needs.
You cannot mix the two gauge and sending unit types. The later type gauge(your BF2223/00) will need the voltage stabilizer, and cannot work with the early sending unit. The early type gauge cannot work on cars with the later sending unit and voltage stabilizer.