i know yours is a C body but hear me out
on the A body there is a pull switch
pull1 = side lights
pull 2 = dipped
pull2 + floor switch = main beam
twist lft for interior light and brightness of dash bulbs
The headlight switch has a overload protection system in it. after a while the overload protection system gets faulty and assumes any load is overload.... basically the bi metallic cut out fatigues and cuts out too easily.
cold bulbs draw more current so the moment you switch on it trips off....
this happens intermittently and gets worse with age until you find you can't get the lights to come on at all.
or they come on 1-2 or 5 minutes after you pull the switch to on
new headlamp switch is the key
get a good one made by the oem and never have an issue again
however your C body won't have that pull switch it will have some kind of flip up and down thing i would think
it may however have the same daft bi metallic protection circuit in it, (chrysler were usually predictable with this stuff), which goes faulty just like the rest of them.
you can mask the issue with a relay if the relay you use uses lower current in its coils than the 2 headlamp bulbs use. you have then made it less likely to trip out due to load the instant you switch on, but your lights are still depending on an old fatigued overload protection thingy.
other candidates are
the earth lead to the bucket of one of the headlamps
the wiring to the foot switch or indeed its connector which are often melted to the point where one of the outermost female connectors can short on the switch case
Dave
