Passenger headlight blinks off and on with my '05 Cadillac CTS

The main fuse box for your CTS is located under the hood. This video shows where to locate it https://www.youtube.com/watch?v=l9-OcTxt-Cw and this site shows the diagram with the fuses and relays https://automobilediagram.com/cadillac-cts-2008-2013-engine-compartment-fuse-diagram-cts-coupe-and-sedan we hope this info helps!

you have a bad stepper motor or bad control unit

Try replacing ALL directionals for the side that is not working properly. That fast blink in the back usually means bad bulb, but could also mean bad relay.

Can you elaborate? You say emergency flashers work, but FR directional does not. Does the bulb-in-question light when the E-flashers are going?

Reads like it is a problem for an auto electrician or someone with access to the vehicles wiring diagram - presumably at some point two circuits are crossing. More likely if it is a modern car, it maybe a bit of computerised hardware that needs a fix or replacement.

relays or fuses or motors can only be one of these

Drivers side is 2-4-6 and passenger side is 1-3-5.
Cylinder 3 should be the middle cylinder on the passenger side.

duplicate question

I think based on the symptoms you need a transmission overhaul.

IF you get a chance check down where your wire harness plugs into your ECM or PCM and see if there is any wire chafe going on down there from when the engine rocks. When it get humid out the wires cross shorting out eachother.

the computer knows that input data from a system has a problem,so disconnecting the battery will not help.
that is the procedure for working on it so that the airbags do not deploy.
a code scanner will tell you which part of the system,including a seatbelt latch,tensioner, or seat position sensor is defective.