On a stock Heritage, this is how the system works.
1. The lights come on when the ignition is turned on to the first position. If they do not, the jumper on the ignition switch has been removed. With the jumper removed the lights come on with the second click of the ignition switch. I have done this change and it is no big deal.
2. The front turn signals are dual filament bulbs. They use the 1157 bulb which has off set bayonets and two contacts on the bulb and two in the bulb socket. One filament is on as running lights with the lights on and the other filament is the turn signal. This is the same bulb used in brake light.
3. The rear turn signals use a signal filament bulb. On a stock bike it is only a turn signal. The bulb has a single contact in the center of the bulb as does the socket. The bayonets are opposite each other on the bulb. If you have dual filament bulb in the rear, and the socket has two contacts, somebody has changed out the rear turn signal housings. If the rear turn signal housings have been changed, in order for them to work, one filament has to have been wired either to the tail light or the brake light while the other one would still act as the turn signal. If you still have signal filament bulbs in the rear, the other option is the adapter H-D sells that turns your rear turn signals into brake lights. It is wired in between the rear fender connectors under the seat and will be a 1 ¼ inch square black module. It does not turn you rear signals into running light only brake lights.
4. The brake light switches are normally open switches. When the brakes are applied, the switch closes, activating the brake lights. If the front brake light switch was replaced, it could have been positioned incorrectly allowing it to stay closed and the brake lever, when all the way out, never allows the switch to go to the open position turning off the brake lights. Check to be sure the master cylinder assembly is properly positioned with the throttle control.
To check the rear switch, turn on the ignition switch and measure the voltage on the switch terminals. One side should have 12 volts, the Orange wire, and the other side, the Red wire, should be almost 0 volts. Apply the rear brake; both sides of the switch wires should now read 12 volts. If they do not the switch is stuck open and will need to be replaced. If they both read 12 volts before applying the brake, the switch is stuck closed and will need to be replaced. If they both read 12 volts, turn off the ignition, pull the red wire off the rear brake light switch, and turn the ignition back on. Verify the brake lights went off. If they went off verify proper operation of the front brake light switch.
All this assumes you have inspected and replaced the bulbs with the proper type and style for the sockets on the bike.
Hope this helps.
