The overdrive is basically a one-speed automatic transmission bolted up the rear of the gearbox.

The overdrive is actuated hydraulically by a piston in the solenoid that opens and closes to control the pressure of the transmission fluid. When the piston is closed, most of the fluid is recirculated through a reservoir to maintain just enough pressure inside of the overdrive so that the moving parts are lubricated. When the piston opens, the fluid is allowed to flow through a relief hole into the overdrive unit which increases the fluid pressure against a set of small pistons inside of the O/D box that push on the springs holding the conical clutch. When there is no pressure on the springs (actuating piston in the solenoid is closed), the conical clutch is fixed to the annulus which gives you a 1:1 gear ratio. When the actuating piston opens, the pressure on the springs engages a brake ring to stop the sun wheel and viola....the annulus is now turning faster than the cone clutch. How much faster is a function of the planetary gear running on the sun wheel.

So, if you are sure that the problem is not electrical (check the wire feeding the solenoid), then you have a leak due to bad seals or the piston has collected metal shavings and can't move a full stroke. Either way you'd have to dig into the transmission as the overdrive is in the same enclosure/body as the gearbox on an automatic car.