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2nd Gen Ram Tech1994-2001 Rams: This section is for TECHNICAL discussions only, that involve the 1994 through 2001 Rams. For any non-tech discussions, please direct your attention to the "General discussion/NON-tech" sub sections.
Probably the wiring behind the switch, or, the multi-function switch on the column.... (turn signal/dimmer switch, etc.) Try tilting your wheel all the way down, and see if they work.
To check the switch you'll need an ohmeter. Just check that there is low resistance between the input terminal ('B1') and output terminal ('H') when the switch is pulled out (headlights on) and should be high resistance otherwise.
The wiring diagrams also show that you may want to also test B2 to I. They also seem to work with your headlights.
I don't know about the resistance but when something like that goes bad in my truck I try tapping it and so far it's fixed my headlight switch and blower motor, the problem is probably in the switch. A thread just got bumped where a guy with a van had to clean his, I just tapped mine with the switch pulled out and got the lights on but later the switch started to melt the connector and had to replace. Since its easy to get to I'd start by looking at that if adjusting your colum doesn't find the problem