Turn Signal/Headlight Malfunction

I have a 2002 Dodge Ram 1500 Sport Quad Cab 4WD that I recently bought
off a friend. He's had this same issue with the truck when I bought it. Here's
what's going wrong:

Whenever I put the turn signal on (left or right doesn't matter) the headlights
will flash twice, and sometimes the wipers will randomly cycle and the horn
will blow. The "Low Wiper Fluid" light also flashes on the panel. It's quite
strange to explain without having a video of it or seeing it in person.

Before I bought it my friend had replaced the turn signal stalk, which didn't
cure the issue. There's also an aftermarket alarm/remote start system that's
tied in with the power locks too. When the lights flash when putting the turn
signal on they flash with the same pattern as when locking the door with the
aftermarket key fob.

Could it be a ground issue that's some how tied in with the alarm system? It's
only started happening in the last several months, and the alarm/remote start
system has been on for several years. Should I start by checking the wiring
in the steering column?

Trying to find a good starting point before I get in over my head, or before I
take it to someone more knowledgeable and spend money unnecessarily.