"Pigtails" is somewhat of a slang term, but if you go to the auto-parts store and look at their replacement connectors, you'll see their connecting wires rolled in a circle. When you unwrap them, the wire retains that shape; when stretched out a bit, it resembles the tail of a pig! It's really just a term for a harness connector or connection(s) that you trim to suitable length.

And yes, you only need one splice into the positive; that goes to the fuse, then the switch, and then you pigtail from there. For the grounding, you can either drill a small hole into metal and use a sheet metal screw, or connect it to a pigtail on the negative (black) lead to your cig lighter.

12.5V when off, eh? That means your battery is not fully charged. Having your vehicle's battery in a partially discharged state means that sulfation (corrosion) of the plates is occurring, and it's life will be shorter than it could be. Your alternator putting out 14.2V confirms the discharged state of your battery. Use Ohm's Law to find out how much current would've been going through your LED's if you'd used the original resistors!

 

I got in my LEDs today. 100 white and 100 blue, with 200 resistors in 3 values. Haven't started making any of my strings yet, but I will definately get a start tomorrow. I also picked up a switch and some insulated quick disconnects today. The only thing I'm missing is the fuse. I looked all around for a 1/4 Amp fuse, but to no avail. The smallest I found were 1 Amp ones. Any other suggestions?
I won't start doing the installing of the lights till next week, so I'll just be busy soldering and making strings this weekend.

 

As much as I loath and despise Radio Shack, they do carry 1/4 Amp fuses.

 

I had checked RS before, but didn't see them. I'll go check again and ask the sales associate/

 

I found a 1/4 Amp fuse, but there was no correct amp size fuse holder. There was a fuse holder rated at 5 Amps, but the associate told me I should find one with a lower rating, closer to 1/4 Amp. I'm wondering if this is necessary. If so I will need to look online because there are none available here.
I had also seen a .315 Amp fuse, and was wondering if I could use this as an upgrade over the 1/4 Amp fuse in case I wanted to run more then 12 strings of LEDs.
But whatever fuse I end up using, I'm stuck on the fuse holder.

 

As long as the fuse holder

1) will correctly fit the fuse mechanically

and

2) is rated for not less than the fuse amperage

it will work find and last a long time.

 

Shoots, sounds good. It was the correct size, but the guy telling me to find a smaller fuse holder was kinda weird. I don't even know if they make 1/4 Amp holders. Well they probably do, but I was figuring that a 5 Amp rated holder would be good enough. And like you said, as long as the holder is rated higher than the fuse.