One thing I have found over the years that causes the BW overdrives to function poorly is the solenoid not getting enough current to kick in. Most problems are with the relay that is mounted on the firewall. When a relays were new you would see the same voltage on the output as what was on the input when the relay was energized. If you bench test an old relay, with it energized, in most cases you will see a large voltage drop between the ign. (input from the ign switch) and the output to the solenoid. The main culprit is at the input fuse holder which is held on by a rivet on each end. When you tighten the screw for the wire terminal that attaches to the fuse holder, it will twist the holder on that rivet and over time will become loose and thus a voltage drop. If you remove the relay cover you will see all connections in the circuit are connected by a similar rivet which can also cause a voltage drop.
The fix to this problem is to clean around all rivet connections and using a good flux, (I use a liquid flux that is used with soldering stain glass), and a good soldering iron, solder the rivet to the surrounding metal. I have done this on many relays and it solved the problem.
Also there could be a voltage drop through your ign. switch due to age and wear so check the voltage from the ign. switch to the relay. It should be the same as the battery.