I remember having that same problem on my truck. After I put the headlight relay harness on, I think that issue went away, but I'm not remembering for certain if that's the case. Since I'm not remembering correctly, maybe that means the relay harness fixed that for me.
If your truck doesn't have a relay harness, definitely add one. They aren't too expensive, easy to install, and well worth the money. The stock headlights in my truck got way brighter with the relays. One of them burned out a couple weeks later, but then I was able to swap to some halogen bulbs which were even better. At the moment, my c10 throws better light than my 95 Dakota. Apparently, Dodge didn't start using headlight relays until some time after 1995, so that'll have to get fixed at some point too
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Christian Carpenter
1963 C10 -
Frankentruck 283, Muncie 3 speed with overdrive
Overdrive wiring here
1963-ish truck bed trailer -
Half-Wit
1981 C10 -
Penny 305, th350 --> Soon to be 350, Saginaw 4 speed
1995 Dodge Dakota Sport
"I'll put it simple: if you're going hard enough left, you'll find yourself turning right." - Doc Hudson