"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!
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!