1997 Ford F150 P0750 and P0500 Codes: Shift Hunting Between Drive and Overdrive?

Hi everyone, I'm new to this forum but have a long history in automotive repair—over 30 years as a diesel mechanic, with extensive experience in gasoline vehicles too. I'm currently working on a 1997 Ford F15-0 4.6L V8, 4WD automatic transmission vehicle. The owner reports that the truck requires easing off the throttle to engage overdrive (OD), and once engaged, it constantly hunts between drive and overdrive. The only transmission-related diagnostic code pulled is P0750 — Shift Solenoid Circuit Fault for Solenoid #1. I'm wondering if this solenoid directly controls overdrive shifting. Is there a direct relationship between the P0750 fault and the erratic shifting behavior? Additionally, the vehicle shows a P0500 code indicating a VSS (Vehicle Speed Sensor) circuit fault. While I suspect it's likely due to a wiring issue or a faulty sensor located on the rear differential, I want to confirm whether this could be contributing to the shifting problems. I'm not convinced that a full transmission replacement is necessary—could these codes point to a more specific repair? Any insights into how P0750 affects overdrive behavior and whether it's one issue or two separate faults would be greatly appreciated. Thanks in advance! — Jeff Smith