Hi Richard,
My guess is that your signal (winker) circuit is drawing too much current and overheating the bimetal spring or relay in the flasher causing it to fuse closed, hence the lights staying on and not winking.
To test the circuit, assuming you have a volt-ohm-ammeter. With the ignition on and the turn signal set either to left or right, measure the voltage at each terminal lug of the relay socket with the other meter lead going to ground. Read the volts and if it is above 10 volts, you have found the switch side of the relay. If it reads no volts, then try switching the switch to see if voltage appears. If not, that terminal lug runs to the lights (supplies the positive to the bulbs). With no voltage reading either way the switch is set, then you need to move to the other terminal lug. Repeat the first prior test and you should see voltage (because your lights stay on.) Turn the signal switch to off, and the voltage should drop to zero. Turn the switch to the other direction and the voltage should be above 10 volts.
Set the meter to read ohms (resistance.) Measuring now from the other terminal lug of the relay socket, measure the resistance (ohms setting on the meter) and if the meter reads infinite or very high ohms (>1000 ohms) you have an open circuit (but this is unlikely because your lights stay ON.) If the resistance to ground is above about 6 ohms, your light circuit is OK, however, if the resistance is very low (<3 ohms) you may have a short to ground which is the cause of the high current flow burning out your relay. If you determine you have a short, you will need to trace the leads to lights emanating from the relay, separate each wire from the circuit, and then test.
If the wiring has been messed with, it's possible that the "Y" terminal that splits the power coming out of the relay could have an additional wire to some other part of the bike hooked up to it. In that case, you will need to hunt around the circuit in the headlamp shell. You are looking for the light blue and orange wires which split at a "Y" terminal in the headlamp shell.
I've included a copy of the wiring schematic to help guide you. Post again if you need further help or just to let me know whether this diagnostic worked for you.
Thanks,
Anna ('78 CB750A - currently down to the frame for restoration)