Headlight relay question

Hey Guys,
I'm new to the forum and have a mysterious malfunction I hope someone can help with. About once every two months my headlights just come on by themselves in the middle of the night or while I'm at work, and drain the battery. I say WTF!, charge the battery, and drive around for another two months until it happens again. I pulled out the headlight relay, looked at it, even pried the cover off of it and it appears clean and happy and functions perfectly-- I can't reproduce the problem at will. With the truck off, headlight switch in the off position, and the relay out, I checked the voltage across both sets of relay terminals. As expected the terminals actually sending power to the lights reads 12.8 volts. The other set that receive power from the headlight switch read 5 volts. I was guessing that set would have no volts with the headlight switch in the off position. Is 5 volts normal? Seems fishy. Could somebody go out and stick a volt meter across those terminals on their truck and tell me what it reads?
Thanks a ton!
Paul
2001 SR5 4x4