The 1947 - Present Chevrolet & GMC Truck Message Board Network - 67 Stepside Front Park/Turn Signals not working

For the 1967 Model Year that is normal. The Parking Lights come on with the first click of the Headlight Switch, and go off with the second click for the big Headlights. [Unless I misread your question, and the front Parking lights are totally dead at all times.]*
They should blink as directional signals when indicating a Left or Right turn by selecting the turn signal lever up or down. They should both blink in unison on Hazard by depressing the button on the Column.

I drove a '68 C/10 Stepside for 20 years before I bought a '67 K/10 Suburban. I thought something was wrong with the wiring until I saw an Orange Stepside much like my own '68, but a '67 [no side markers] outside a bar. Being one of my former undergraduate hangouts, I inquired inside, and it was the bartender's truck. Over a beer, I explained my '67 Sub's ''gripe'' and he said that's how it was for that year. We went out to the parking lot, and sure enough, his stepside had no yellow "Running Lights" when the Headlight Switch went to 2nd click. And that was normal. This was before the internet, obviously.

In 1968, Federal regulations mandated they become Running Lights, and stay on with the headlights. Also Side Marker Reflectors were mandated. '69 MY, the Side Markers were optionally illuminated, and by '71 MY they were illuminated as Standard, and the front side markers blinked alternately with the front Running Lights when indicating turns.

* If you have totally dead lights, it could be the bulbs, corrosion inside the bulb sockets, opens in the wiring to the light buckets, bad grounds, or any-and-all of the above.