Power drain and clicking sound when Dodge Dakota is off

There is a clicking sound (about once per second) in the front of the engine compartment of my 2002 Dodge Dakota (2WD, quad cab, manual, no alarm, no electric windows, locks, mirrors, etc.) when the vehicle is off (ignition in the off position - with or without key in ignition). It stops if the battery is disconnected, if the key is in the run position, or if the key is in the position that allows one to use power while the vehicle is off. The interior lights and headlights will flash in sync with the clicking sound if they are on as well. The chime that lets you know that the key is in the ingnition with the door open will miss a beat with the click also. The amps running through the circuit (no lights on) jump up from 27 milliamps to 39 milliamps with the click sound. A possibly related issue is that the headlights no longer stay on for the 30 seconds or so that they used to when I turn off and exit the truck after having driven with the lights on.
The clicking and light flashing continued even though I removed each fuse and relay in the box under the hood and the one next to the driver door (the lights stopped when their fuse was removed, but the clicking continued). Any thoughts about what this could be would be greatly appreciated.
Thank you.

Sound like the Central Timer Module has failed, a common problem on Dakotas. The CTM controls the interior lights, head lights, RKE and power door locks.
Remove the left kick panel (next to the parking brake) and unplug the module, the lights should stop flashing. You can replace this module yourself.

It sounds like there may be something going on with the alarm system or panic alarm. Did you try locking the doors with the keyfob to see if that stops the problem?

I disconnected the Central Timer Module and the clicking sound stopped. I will replace the module and see see if that solves the problem. Thank you for your responses.