Wikipedia says that Indiction began in 3rd Century Roman Egypt, and was used for tax-collection:
Indictions originally referred to the periodic reassessment for an agricultural or land tax in late third-century Roman Egypt
At the same time, Egypt had a similar tradition of cattle-counting, originating from the Old Kingdom, which was similarly used for tax purposes, and was also used for dating.
Are they related? Did the indiction as practiced in Roman Egypt represent an unbroken tradition of cattle-count? Or was it discontinuous?
It's unlikely that they are anything more than loosely connected given the massive span of time between the Old Kingdom and the late third century CE. Surely each succeeding dynasty in Egypt took over and adapted pre-existing institutions to varying decrees, but the only connection I can see is that cattle counting and indictions are both dating systems based on annual state assessments. The indiction system, moreover, became a 15-year cycle in the early fourth century CE, which does not find a parallel in the earlier cattle counting system.
Sources:
Hornung, Krauss, and Warburton, Ancient Egyptian Chronology (Leiden/Boston 2006).
Bagnall and Worp, Chronological Systems of Byzantine Egypt: Second Edition (Leiden 2004)
Thomas, "Epigraphai and Indictions in the Reign of Diocletian," Bulletin of the American Society of Papyrologists 15 (1978), 133-145.