No, the headlight relay setup only handles the headlamps.  If you wanted to run the marker lights on a relay, you'd have to add a different one.  But, since the marker light bulbs are only 5w each, even if there's a city light in the headlamp, front and rear side markers, and tail light, that's only 20 watts per side, or 40 watts total, compared to 60 watts each headlight bulb (120W total) on high beam.  So the side markers probably don't need a relay.  But they SHOULD be properly wired.  I think it's okay for the front side marker to come off the headlamp city light, and for the rear side marker to come off the rear park light wire for the given side.  You'll probably have fun trying to solder those wires up.  Lots of times they're corroded pretty badly.  But keep after it with a little 600 grit sandpaper (spread the strands of the wire out and draw the "fan" between two sheets of sandpaper) and you should be abel to get the wires to "tin" (solder to wet to them).  The cut ground wire there is probably coming from the side marker and they've left the marker lamp to ground through it's housing being screwed to the body.  Just a guess.

Keep after it!

-Dave G.

Crimping is fine if it's done right.  Trouble is most generic crimping tools don't do it right.  Most are equivalent to "smash it with a pliers" and these will loosen up over time, let corrosion build inside between wires and connector, etc.

I have one like this:

http://www.hardwarestore.com/media/product/601530_front500.jpg

And when using good quality tinned copper connectors, oriented with the split side into the female jaw, I've never had a problem with any of them coming loose.

Stay away from this kind:

http://www.hardwarestore.com/media/product/266668_front500.jpg

that just pinch the connector flat.

There's an even better kind that ratchet closed so that you MUST complete the crimp before the jaws will open.  These are required for mil spec crimps, but are very specific for connector type and wire gauge, and a little impractical for the shardetree guy.  Like I said, I use some like the ones in the first reference to crimp terminations (not wire to wire if I can help it) and I've not had  problem with those crimps yet.

The observatoin Karl made is a good one, that a solder joint stiffens the wire.  But then, so does the crimp, and the barrel of the crimp adds more mass to the assembly than the solder does.  The bottom line is that it's a secondary feature of the heat shrink tubing that it acts as a strain relief at the interface where the wire compliance changes, whether that be at the end of the crimp connector, or at the point the solder joint stops.  So save some money when you buy your crimp sleeves.  Buy the un-insulated kind and slip the adhesive lined heat shrink over them to get the dual purpose role of insulation plus strain relief.

If you get into the WeatherPac stuff you'll see how those terminals are crimped 2x.  Once to the bare wire, and then a little upstream, to the insulated portion of the wire, and then upstream of THAT they go through the moisture barrier bushing.  A real nice design.

Sorry, I'm rambling.....

-Dave G.