P0501 Code Intermittent in 1998 VW Jetta: Is Missing Transmission Tooth a Plausible Cause?

I am the second owner of a 1998 Volkswagen Jetta 4-cylinder, 5-speed manual transmission. This vehicle has consistently shown Diagnostic Trouble Code (DTC) P0501 for over several years. The Check Engine Light (CEL) typically flickers on and off, remaining lit for approximately 11 months of the year. While it occasionally turns itself off and the vehicle displays 'ready' status across all systems, it has passed annual emissions inspections every year. The primary symptom is that the speedometer reads 0 mph continuously—however, I verify actual speed using my tachometer and GPS, confirming the issue is not with the speedometer display. I have already replaced the vehicle's speed sensor without resolving the problem. A previous garage inspection suggested that a missing tooth or piece in the internal transmission gear where the speed sensor contacts it may be causing intermittent signal loss. They advised against repair due to the intermittent nature and high cost of such work. I deeply love this car, having recently restored it with original Volkswagen factory paint. With my next inspection scheduled for May, I am concerned that if the vehicle fails, I will qualify for a one-year waiver since the issue is not safety-related. Does this diagnosis—specifically, a missing tooth in the transmission gear—seem plausible? The repair facility is a general auto shop, not a specialized transmission service. Should I consider selling before my sticker expiration, despite my strong emotional attachment to the vehicle, or is there a viable fix available? Thank you for any insights or experiences with this issue on 1998 VW Jetta models.