Why does the overdrive on and off button flash in a 2000 Ford F-250 supeduty 4x4 liarit?

Why does the overdrive on and off button flash in a 2000 Ford F-250 supeduty 4x4 liarit? - 1

Because a fault with the transmission is being detected.

Yes a fault is occuring with the transmission. Usually an issue with the solenoids, however you can access and change the solenoids when you drain and drop the transmission pan in those 4R100 transmissions.