’99 Durango interior electrical issues

It sounds like you have a couple of issues that may not be related. The lites that come on when you try to brighten with the light switch, the portion of the light switch that brightens the interior lites is a ground circuit that runs through a varible resistor, as you move the thumb wheel up or turn the knob the ground resitance is reduced and thus the lites become brighter. at the end of the travel of the lite switch variable resistor is a terminable that is full ground and is attached to the interior lighting. turning the knob or thum wheel to its brightest point will ground the interior courtesy light circuit,and cause the interior lites to come on. I would begin my inspection with checking this switch.
as for the lites going off when you touch the equalizer buttons, either the bulbs are loose or a bad ground or poor electrical connection in the circuit that feed the lites would be what I would check first.
ON the tail lite issue you may want to start by pulling out the bulbs on the side that is showing a fast clicking, I supect that one or more of the tail lite bulbs has shorted internally. when you pull the bulbs out you should be able to tell rather quickly if this is the case. If that passes then check the turn signal flasher. a weak flasher could cause the same problem.

for the quick blinking.you may have a blinker
bulb out.Turn the blinker on each side and look
outside to see if the front and back are on and
blinking.if not replace the bulb.