Front indicators

Just bought a KZ650b needs some TLC, hooked it up to a battery just to see what works, everything lights up okay but both front indicators come on along with the headlight? Is that normal for a USA spec bike? There is no on off switch for the lights? I'm in the UK.

Yes, that's normal in the USA. The front turn signals have 2-filament bulbs >> 1 filament for the running lights & a 2nd filament for the turn signals. The rear turn signals have 1-filament bulbs.

Those front indicators being on with the headlight is normal. Please state the year of the bike. The 1977 KZ650 had a on/off switch for headlights; later models did not. Ed

Ive got a 78 KZ650 B and it has an on off switch for the light lights. My issue is that the right side blinkers blink, but the left side just come on and stay steady.
Is there a relay or something I'm missing?

Have you replaced any bulbs recently? Modern bulbs may not work right with the old turn signal flasher >> the fix would be to install an electronic flasher. Autozone & other places have Novita electro-mechanical flashers that are physically almost identical to the original oem flashers. I would make sure the front left bulb is good, ie, the turn signal filament isn't bad. You could also swap one or both bulbs to see if the problem follows the bulbs.