From OP's description, it seems the lighting is working as designed, at least for a US-spec bike. The parking light is exactly that; motor off but tail light filament energized for conspicuity when parked.
If OP is looking for modern front-facing conspicuity, similar to the front turn signals running lights on more modern bikes, consider mounting a pair of small LED lights in place of the reflectors that are on the front downtube brackets. They'd be easy to mount and, easy to connect without butchering the wiring harness and/or adapting other front turn signals.
slmjim & Z1BEBE
A biker looks at your engine and chrome.
A Rider looks at your odometer and tags.
When the ignition switch is set to ON, the tail light should be lighted then get brighter when the brake is applied.
If the tail light doesn't work when the ignition switch is ON, but lights in PARK, then that sounds like a problem at the ignition switch.
maybe a broken solder joint between blue & red inside the switch. ??? see the wiring diagram w continuity table at the bottom. diagrams.kz650.info/wiring/images/KZ650-D1.jpg
You may need to check the legality of adding running lights to the rear.
I cant see anyone caring about more lighting on the rear. I wasn't aware that the brake light filament wasalso the running light. Thats odd but interesting. So I'm assuming it gets less voltage ? I'm not really seeing that. My ignition switch seems to be working as designed. In ON the brake light circuit is open until a brake is applied then it closes lighting the light, the PARK circuit oy gets power at rhe second position of the key. What I was wanting is already on many many newer bikes, the rear has three running lights and the turn signals over ride the running light at does the brake. So what I've added is LED turn signals and they have a built in red light, and go segmented orange on turn signal. I was thinking of using them as additional brake lights, and the single brake light as the only running light. I agree the original light had license plate clear lens.... so what you're saying certainly jibes with what I have. I was contemplating tieing in the PARK light feature to the brake light circuit with a zener diode on it. S9 when in park I would get all three lights at the rear, but the brake circuit wouldn't be pushing power back at the ignition. Then I'd tie in an ON position power to the running light lead,. Ill review the drawings much appreciated. I'm not concerned about the factory harness as it had so many poor solder joints in it its no longer much like a factory harness I maintained the colors but its been modified to make more sense and to prevent breaks and resistance from poor connectors. Not to mention weather proofed. It rains a lot here.
The 1978 650 SR models are either D1or D1A, the only real difference between them is the size of the carbs which came stock on them. Both have front running lights but no rear (other than tail light) running lights. Not sure if you have a wiring diagram for your bike but here are both below. If you want to add rear running lights you would need to replace the rear turn single sockets to dual filament and dual filament bulbs and add wiring to make them work.
....I wasn't aware that the brake light filament wasalso the running light.
It's not. You have a 'tail light' and a brake light (that's the two-filament bulb - sometimes more than one two-filament bulbs, sometimes separate tail and brake bulbs). The tail light is on whenever your ignition switch is in the ON or the P position. Brake light comes on when you activate the brakes but only while the igntion switch is in the ON position.
uhm thanks? I got all that. My comment was kind of sarcastic in reply to another comment about the bulbs. My bad. It seems people like to offer a lot of opinions rather than offer a solution or experience. Had I realized there was a tail specific fuse, that would have been my first check.
The issue turned out to be simple, I was popping the tail fuse. Due to the front turn signal on the right side being removed it was shorting and also I had put in a temp headlight bulb that was way too powerful to remind me the ignition was on, as the dash isnt on yet and it was over drawing. Now it all works, I have a tail running light and brake light(crap amazon one that I liked the look of) that I also had to add a diode to, in order to block voltage feeding back through it on its brake light lead and lighting the led turn signals up. On brake the turn signals go bright red as does the tail, and the turn signal overrides the brake on the signal if its on. All looks great.