Jason,
You will not find a serial number on this C24 MKI, because its housing tube was changed out, many years after it was issued. And, unlike most C12, there was no additional serial number embossed on this model's connector barrel.
From the photos it looks like it's been extensively serviced by James Gangwer in the East Bay. I would therefore strongly advise to contact him: some C24 refurbished with replacement housings (which were likely supplied by AKG, or the mic was serviced by AKG) may also miss the original CK12 capsules*, with Teflon/Nylon CK12 as replacement, so he may have more information.
*James probably would not have done that- he is meticulous about restorations and respects authenticity in vintage mics- but it may have been done at some time prior.